Question 1: Palette 1/89

Objective Physics Vol-1 MCQ

Concept: Dimensional Analysis

Find the dimensional formula of coefficient of viscosity, $\eta$, given $F = -\eta A \left(\frac{\Delta v}{\Delta l}\right)$, where $F$ is force, $A$ is area, $\Delta v$ is velocity, and $\Delta l$ is length.

A

$[M^1 L^{-1} T^{-1}]$

B

$[M^1 L^2 T^{-2}]$

C

$[M^1 L^{-2} T^{-1}]$

D

$[M^0 L^1 T^{-2}]$

Question 2: Palette 2/89

Objective Physics Vol-1 MCQ

Find the dimensional formula of charge, $q$, given $q = I t$, where $I$ is electric current and $t$ is time.

A

$[M^0 L^0 T^1 A^1]$

B

$[M^1 L^0 T^{-1} A^1]$

C

$[M^0 L^1 T^1 A^{-1}]$

D

$[M^1 L^1 T^0 A^1]$

Question 3: Palette 3/89

Objective Physics Vol-1 MCQ

Find the dimensional formula of electric potential, $V$, given $U = V I t$, where $U$ is energy, $I$ is electric current, and $t$ is time.

A

$[M^1 L^1 T^{-2} A^{-1}]$

B

$[M^1 L^2 T^{-3} A^{-1}]$

C

$[M^1 L^2 T^{-2} A^1]$

D

$[M^0 L^2 T^{-3} A^{-1}]$

Question 4: Palette 4/89

Objective Physics Vol-1 MCQ

Find the dimensional formula of capacitance, $C$, given $q = C V$, where $q$ is charge and $V$ is electric potential.

A

$[M^1 L^2 T^{-4} A^{-2}]$

B

$[M^{-1} L^{-2} T^3 A^1]$

C

$[M^{-1} L^{-2} T^4 A^2]$

D

$[M^0 L^{-2} T^4 A^1]$

Question 5: Palette 5/89

Objective Physics Vol-1 MCQ

Find the dimensional formula of resistance, $R$, given $V = I R$, where $V$ is electric potential and $I$ is electric current.

A

$[M^1 L^2 T^{-3} A^{-2}]$

B

$[M^1 L^1 T^{-3} A^{-1}]$

C

$[M^1 L^2 T^{-2} A^{-2}]$

D

$[M^{-1} L^2 T^{-3} A^{-2}]$

Question 6: Palette 6/89

Objective Physics Vol-1 MCQ

If $C$ and $R$ denote capacitance and resistance respectively, find the dimensions of $CR$.

A

$[M^0 L^0 T^1 A^0]$

B

$[M^1 L^2 T^{-3} A^{-1}]$

C

$[M^{-1} L^{-2} T^4 A^2]$

D

$[M^1 L^0 T^{-1} A^0]$

Question 7: Palette 7/89

Objective Physics Vol-1 MCQ

Which amongst the following quantities is (are) dimensionless?

A

Ratio of work to energy

B

$\sin\theta$

C

Ratio of momentum to time

D

Both A and B

Question 8: Palette 8/89

Objective Physics Vol-1 MCQ

In the formula $x = 3yz^2$, if $x$ and $y$ have the dimensions of capacitance and magnetic induction respectively, find the dimensions of $y$.

A

$[M^{-3} L^2 T^{-8} A^{-4}]$

B

$[M^3 L^2 T^8 A^4]$

C

$[M^3 L^{-2} T^8 A^4]$

D

$[M^{-3} L^{-2} T^8 A^4]$

Question 9: Palette 9/89

Objective Physics Vol-1 MCQ

Write the dimensions of $a$ and $b$ in the relation $P = \frac{b - x^2}{at}$, where $P$ is power, $x$ is distance, and $t$ is time.

A

$[a] = [M^{-1} L^0 T^2]$ and $[b] = [M^0 L^2 T^0]$

B

$[a] = [M^1 L^2 T^{-3}]$ and $[b] = [M^0 L^1 T^0]$

C

$[a] = [M^{-1} L^2 T^2]$ and $[b] = [M^0 L^2 T^0]$

D

$[a] = [M^{-1} L^0 T^3]$ and $[b] = [M^0 L^1 T^1]$

Question 10: Palette 10/89

Objective Physics Vol-1 MCQ

The velocity $v$ of a particle depends upon the time $t$ according to the equation $v = a + bt + \frac{c}{d + t}$. Write the dimensions of $a$, $b$, $c$, and $d$.

A

$[a] = [L T^{-1}]$, $[b] = [L T^{-2}]$, $[c] = [L]$, $[d] = [T]$

B

$[a] = [L T^{-2}]$, $[b] = [L T^{-1}]$, $[c] = [T]$, $[d] = [L]$

C

$[a] = [L T^{-1}]$, $[b] = [L T^{-1}]$, $[c] = [L T]$, $[d] = [T]$

D

$[a] = [L T^{-2}]$, $[b] = [L T^{-2}]$, $[c] = [L]$, $[d] = [T^{-1}]$

Question 11: Palette 11/89

Objective Physics Vol-1 MCQ

Find the value of $100\text{ J}$ on a system which has $20\text{ cm}$, $250\text{ g}$, and half minute as fundamental units of length, mass, and time.

A

$9 \times 10^4\text{ new units}$

B

$9 \times 10^5\text{ new units}$

C

$9 \times 10^6\text{ new units}$

D

$9 \times 10^7\text{ new units}$

Question 12: Palette 12/89

Objective Physics Vol-1 MCQ

The value of gravitational constant is $G = 6.67 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2$ in SI units. Convert it into CGS system of units.

A

$6.67 \times 10^{-6}\text{ dyne}\cdot\text{cm}^2/\text{g}^2$

B

$6.67 \times 10^{-8}\text{ dyne}\cdot\text{cm}^2/\text{g}^2$

C

$6.67 \times 10^{-10}\text{ dyne}\cdot\text{cm}^2/\text{g}^2$

D

$6.67 \times 10^{-11}\text{ dyne}\cdot\text{cm}^2/\text{g}^2$

Question 13: Palette 13/89

Objective Physics Vol-1 MCQ

The frequency $f$ of a stretched string depends upon the tension $F$ (force), length $l$ of the string, and mass per unit length $\mu$ of the string. Derive the expression for frequency using dimensional analysis.

A

$f = \frac{k}{l^2} \sqrt{\frac{F}{\mu}}$

B

$f = \frac{k}{l} \sqrt{\frac{F}{\mu}}$

C

$f = k l \sqrt{\frac{\mu}{F}}$

D

$f = \frac{k}{l} \sqrt{\frac{\mu}{F}}$

Question 14: Palette 14/89

Objective Physics Vol-1 MCQ

The centripetal force $F$ acting on a particle moving uniformly in a circle may depend upon mass $m$, velocity $v$, and radius $r$ of the circle. Derive the formula for $F$ using the method of dimensions.

A

$F = \frac{m v^2}{r^2}$

B

$F = \frac{m v^2}{r}$

C

$F = \frac{m^2 v}{r}$

D

$F = \frac{m v}{r^2}$

Question 15: Palette 15/89

Objective Physics Vol-1 MCQ

In the SI system, the unit of temperature is

A

degree centigrade

B

kelvin

C

degree celsius

D

degree Fahrenheit

Question 16: Palette 16/89

Objective Physics Vol-1 MCQ

Concept: Power is defined as the rate at which work is done or energy is transferred. In electrical circuits, power can be expressed in terms of voltage, current, and resistance using formulas derived from Ohm's law.

Which amongst the following is not equal to watt?

A

joule/second

B

ampere x volt

C

$(\text{ampere})^2 \times \text{ohm}$

D

ampere/volt

Question 17: Palette 17/89

Objective Physics Vol-1 MCQ

Concept: The unit of a physical quantity can be determined by analyzing its fundamental relation with work, energy, time, or momentum. Planck's constant and angular momentum share the same unit, which is expressed in terms of joule-second.

Joule x second is the unit of

A

energy

B

momentum

C

angular momentum

D

power

Question 18: Palette 18/89

Objective Physics Vol-1 MCQ

Concept: Two physical quantities possess the same units if they describe similar physical properties or are defined by proportional relations involving the same fundamental quantities.

Which amongst the following pairs has the same units?

A

Wavelength and Rydberg constant

B

Relative velocity and relative density

C

Thermal capacity and Boltzmann constant

D

Time period and acceleration gradient

Question 19: Palette 19/89

Objective Physics Vol-1 MCQ

Concept: To convert a physical quantity from one system of units to another, the numerical value $n$ and unit $u$ satisfy $n_1 u_1 = n_2 u_2$. Convert grams to kilograms ($1\text{ g} = 10^{-3}\text{ kg}$) and centimeters to meters ($1\text{ cm} = 10^{-2}\text{ m}$).

Density of liquid in CGS system is $0.625\text{ g cm}^{-3}$. What is its magnitude in SI system?

A

$0.625$

B

$0.0625$

C

$0.00625$

D

$625$

Question 20: Palette 20/89

Objective Physics Vol-1 MCQ

Concept: Surface tension is defined as the force acting per unit length along an imaginary line drawn on the surface of a liquid. Its dimensional formula is derived from the ratio of the dimensions of force to length.

Dimensions of surface tension are

A

$[\text{M}^2 \text{L}^2 \text{T}^{-2}]$

B

$[\text{M}^2 \text{L} \text{T}^{-2}]$

C

$[\text{M T}^{-2}]$

D

$[\text{M L T}^{-2}]$

Question 21: Palette 21/89

Objective Physics Vol-1 MCQ

Concept: Impulse is defined as the change in momentum of an object when a force acts upon it over a time interval. By the impulse-momentum theorem, impulse and linear momentum share the exact same physical dimensions.

The dimensions of impulse are equal to that of

A

force

B

linear momentum

C

pressure

D

angular momentum

Question 22: Palette 22/89

Objective Physics Vol-1 MCQ

Concept: Pressure is defined as force per unit area. Any quantity whose physical representation cannot be reduced to force per unit area or energy per unit volume will have different dimensions from pressure.

Which of the following does not possess the same dimensions as that of pressure?

A

Stress

B

Bulk modulus

C

Thrust

D

Energy density

Question 23: Palette 23/89

Objective Physics Vol-1 MCQ

Concept: Newton's law of universal gravitation states that the gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The dimensions of the gravitational constant $G$ can be determined by rearranging this force equation.

What is the dimensional formula of gravitational constant?

A

$[\text{M L}^2 \text{T}^{-2}]$

B

$[\text{M L}^{-1} \text{T}^{-1}]$

C

$[\text{M}^{-1} \text{L}^3 \text{T}^{-2}]$

D

None of these

Question 24: Palette 24/89

Objective Physics Vol-1 MCQ

Concept: Two physical quantities possess the same dimensions if they can be expressed using identical combinations of the fundamental units of mass, length, and time. Both torque and potential energy represent quantities related to force acting through a distance.

Which one of the following have same dimensions?

A

Torque and force

B

Potential energy and force

C

Torque and potential energy

D

Planck's constant and linear momentum

Question 25: Palette 25/89

Objective Physics Vol-1 MCQ

Concept: The coefficient of viscosity $\eta$ measures a fluid's resistance to flow. Its dimensional formula can be determined by isolating $\eta$ in Stokes' law equation and substituting the fundamental dimensions of force, length, and velocity.

The force $F$ on a sphere of radius $a$ moving in a medium with velocity $v$ is given by $F = 6\pi \eta a v$. The dimensions of $\eta$ are

A

$[\text{M L}^{-3}]$

B

$[\text{M L T}^{-2}]$

C

$[\text{M T}^{-1}]$

D

$[\text{M L}^{-1} \text{T}^{-1}]$

Question 26: Palette 26/89

Objective Physics Vol-1 MCQ

Concept: Specific resistance (or resistivity, $\rho$) is an intrinsic property of a material given by $\rho = R \frac{A}{l}$, where $R$ is electrical resistance, $A$ is cross-sectional area, and $l$ is length. Resistance can be expressed in terms of work done per unit charge and current.

The dimensional representation of specific resistance in terms of charge $Q$ is

A

$[\text{M L}^3 \text{T}^{-1} \text{Q}^{-2}]$

B

$[\text{M L}^3 \text{T}^{-2} \text{Q}^2]$

C

$[\text{M L T}^{-2} \text{Q}^{-1}]$

D

$[\text{M L}^3 \text{T}^{-1} \text{Q}^{-1}]$

Question 27: Palette 27/89

Objective Physics Vol-1 MCQ

Concept: Planck's constant $h$ relates the energy of a photon to its frequency ($E = h \nu$), while angular momentum $L$ represents the rotational analog of linear momentum ($L = r \times p$). Both physical quantities share identical dimensions.

The dimensional formula for Planck's constant and angular momentum is

A

$[\text{M L}^2 \text{T}^{-2}]$ and $[\text{M L T}^{-1}]$

B

$[\text{M L}^2 \text{T}^{-1}]$ and $[\text{M L}^2 \text{T}^{-1}]$

C

$[\text{M L}^3 \text{T}^{-1}]$ and $[\text{M L}^2 \text{T}^{-2}]$

D

$[\text{M L T}^{-1}]$ and $[\text{M L T}^{-2}]$

Question 28: Palette 28/89

Objective Physics Vol-1 MCQ

Concept: The expression $\frac{1}{2} \varepsilon_0 E^2$ represents the electrostatic energy density, which is defined as the electric energy stored per unit volume in a medium or vacuum. Its dimensional formula can be determined directly by evaluating the ratio of energy to volume.

The dimensions of $\frac{1}{2} \varepsilon_0 E^2$ ($\varepsilon_0$ is the permittivity of the space and $E$ is electric field), are

A

$[\text{M L}^2 \text{T}^{-1}]$

B

$[\text{M L}^{-1} \text{T}^{-2}]$

C

$[\text{M L}^2 \text{T}^{-2}]$

D

$[\text{M L T}^{-1}]$

Question 29: Palette 29/89

Objective Physics Vol-1 MCQ

Concept: When fundamental or derived physical quantities are scaled by certain factors, the scaling factors of other related physical quantities can be determined using their dimensional formulas or defining equations.

The units of length, velocity and force are doubled. Which of the following is the correct change in the other units?

A

Unit of time is doubled

B

Unit of mass is doubled

C

Unit of momentum is doubled

D

Unit of energy is doubled

Question 30: Palette 30/89

Objective Physics Vol-1 MCQ

Concept: In any trigonometric function such as $\cos(\theta)$, the argument $\theta$ must be dimensionless. Consequently, each term inside the argument of the trigonometric function must also be dimensionless.

Given that $y = a \cos \left( \frac{t}{p} - qx \right)$, where $t$ represents time and $x$ represents distance; which amongst the following statements is(are) true?

A

The unit of $x$ is same as that of $q$

B

The unit of $x$ is same as that of $p$

C

The unit of $t$ is same as that of $q$

D

The unit of $t$ is same as that of $p$

Question 31: Palette 31/89

Objective Physics Vol-1 MCQ

Concept: According to the principle of homogeneity of dimensions, quantities with the same dimensions can be added or subtracted from one another. Thus, $a$ must have the same dimensions as $t^2$. Once the dimensions of $a$ and $b$ are determined, the ratio $\frac{a}{b}$ can be evaluated.

The dimensions of $\frac{a}{b}$ in the equation $p = \frac{a - t^2}{bx}$, where $p$ is pressure, $x$ is distance and $t$ is time, are

A

$[\text{M}^2 \text{L T}^{-3}]$

B

$[\text{M T}^{-2}]$

C

$[\text{L T}^{-3}]$

D

$[\text{M L}^3 \text{T}^{-1}]$

Question 32: Palette 32/89

Objective Physics Vol-1 MCQ

Concept: In any trigonometric function like $\sin(\theta)$, the argument $\theta$ must be dimensionless. Therefore, each term inside the bracket being subtracted or added must have the same dimension as the other, or the entire quantity inside the trigonometric function must evaluate to a dimensionless number.

The equation of a wave is given by $y = a \sin \omega \left( \frac{x}{v} - k \right)$, where $\omega$ is angular velocity and $v$ is the linear velocity. The dimensions of $k$ will be

A

$[\text{T}^{-2}]$

B

$[\text{T}^{-1}]$

C

$[\text{T}]$

D

$[\text{LT}]$

Question 33: Palette 33/89

Objective Physics Vol-1 MCQ

Concept: Using the given relationship $\text{Power} = \text{muscle} \times \text{speed}$, we can find the physical dimensions and units of 'muscle'. The conversion factor between the SI unit and CGS unit of any physical quantity can then be determined using its base dimensions of mass, length, and time.

If 'muscle times speed equals power', then what is the ratio of the SI unit and the CGS unit of muscle?

A

$10^5$

B

$10^3$

C

$10^7$

D

$10^{-5}$

Question 34: Palette 34/89

Objective Physics Vol-1 MCQ

Concept: A quantity is dimensionless when the net powers of fundamental dimensions mass $[\text{M}]$, length $[\text{L}]$, and time $[\text{T}]$ are all equal to zero. Equating the sum of powers for each fundamental dimension to zero gives a system of linear equations to determine $x$, $y$, and $z$.

If $p$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then for what values of non-zero integers $x$, $y$ and $z$, $p^x Q^y c^z$ is dimensionless?

A

$x = 1, y = 1, z = -1$

B

$x = 1, y = -1, z = 1$

C

$x = -1, y = 1, z = 1$

D

$x = 1, y = 1, z = 1$

Question 35: Palette 35/89

Objective Physics Vol-1 MCQ

Concept: Using dimensional analysis, a physical quantity can be expressed as a product of powers of other physical quantities. Equating the fundamental dimensions of mass $[\text{M}]$, length $[\text{L}]$, and time $[\text{T}]$ on both sides allows us to find the required power dependence.

Assuming that the mass $m$ of the largest stone that can be moved by a flowing river depends upon the velocity $v$ of the water, its density $\rho$ and the acceleration due to gravity $g$. Then, $m$ is directly proportional to

A

$v^3$

B

$v^4$

C

$v^5$

D

$v^6$

Question 36: Palette 36/89

Objective Physics Vol-1 MCQ

Concept: Significant figures represent the reliable digits in a measurement plus the first uncertain digit. Non-zero digits are always significant, while trailing zeros in a number without a decimal point are not significant.

How many significant figures are present in the measured values $227.2\text{ g}$ and $3600\text{ g}$ respectively?

A

4 and 4

B

4 and 2

C

3 and 2

D

4 and 3

Question 37: Palette 37/89

Objective Physics Vol-1 MCQ

Concept: Leading zeros in a decimal number (zeros before the first non-zero digit) are not significant. In scientific notation, the power of 10 is irrelevant to the count of significant figures, and trailing zeros after a decimal point are significant.

How many significant figures are present in the measured values $0.00602\text{ g}$ and $2.50 \times 10^{10}\text{ g}$ respectively?

A

5 and 2

B

3 and 2

C

3 and 3

D

5 and 3

Question 38: Palette 38/89

Objective Physics Vol-1 MCQ

Concept: When adding or subtracting numbers in scientific notation, first rewrite the quantities so they have the same exponent. The final result must then be rounded off to the same number of decimal places as the quantity having the least number of decimal places.

Add $6.75 \times 10^3\text{ cm}$ to $4.52 \times 10^2\text{ cm}$ with regard to significant figures.

A

$7.2 \times 10^3\text{ cm}$

B

$7.20 \times 10^3\text{ cm}$

C

$7.202 \times 10^3\text{ cm}$

D

$7.2022 \times 10^3\text{ cm}$

Question 39: Palette 39/89

Objective Physics Vol-1 MCQ

Concept: When adding or subtracting measured quantities, the rule of significant figures requires that the final result should contain only as many decimal places as are present in the measurement with the least number of decimal places.

Two sticks of lengths $12.132\text{ cm}$ and $10.2\text{ cm}$ are placed end to end. Find their total length with due regard to significant figures.

A

$22.332\text{ cm}$

B

$22.33\text{ cm}$

C

$22.3\text{ cm}$

D

$22.0\text{ cm}$

Question 40: Palette 40/89

Objective Physics Vol-1 MCQ

Concept: When multiplying or dividing measured quantities, the final result should contain only as many significant figures as are present in the measurement with the least number of significant figures. Power is calculated as $P = V \times I$.

The voltage across a lamp is $6.32\text{ V}$ when the current passing through it is $3.4\text{ A}$. Find the power consumed up to appropriate significant figures.

A

$21.488\text{ W}$

B

$21.5\text{ W}$

C

$21\text{ W}$

D

$21.49\text{ W}$

Question 41: Palette 41/89

Objective Physics Vol-1 MCQ

Concept: The volume of a cylindrical wire is given by $V = \pi r^2 l$. In multiplication, the final result must be reported with the same number of significant figures as the measurement with the least number of significant figures.

A thin wire has a length of $21.7\text{ cm}$ and radius $0.46\text{ mm}$. Calculate the volume of the wire up to correct significant figures.

A

$0.1443\text{ cm}^3$

B

$0.144\text{ cm}^3$

C

$0.14\text{ cm}^3$

D

$0.1\text{ cm}^3$

Question 42: Palette 42/89

Objective Physics Vol-1 MCQ

Concept: The time period $T$ is calculated by dividing the total time taken by the exact number of vibrations. Since the number of vibrations is an exact count, it has an infinite number of significant figures. Therefore, the result of the division must be reported with the same number of significant figures as the measured total time.

The time taken by a pendulum to complete 25 vibrations is $88.0\text{ s}$. Find the time period of the pendulum in seconds up to appropriate significant figures.

A

$3.5\text{ s}$

B

$3.52\text{ s}$

C

$3.520\text{ s}$

D

$4\text{ s}$

Question 43: Palette 43/89

Objective Physics Vol-1 MCQ

Concept: Density is defined as mass per unit volume ($\rho = \frac{\text{mass}}{\text{volume}}$). In multiplication or division of measured quantities, the final result must be rounded off to have as many significant figures as the measurement with the least number of significant figures.

$5.74\text{ g}$ of substance occupies $1.2\text{ cm}^3$. Express its density by keeping the significant figures in view.

A

$4.783\text{ g/cm}^3$

B

$4.78\text{ g/cm}^3$

C

$4.8\text{ g/cm}^3$

D

$5.0\text{ g/cm}^3$

Question 44: Palette 44/89

Objective Physics Vol-1 MCQ

Concept: When rounding off a measurement to a specified number of significant figures:
1. If the digit to be dropped is less than 5, the preceding digit is left unchanged.
2. If the digit to be dropped is greater than 5, the preceding digit is increased by 1.
3. If the digit to be dropped is 5:
* If the preceding digit is even, it remains unchanged.
* If the preceding digit is odd, it is raised by 1.

Round off the following numbers up to three significant figures:
(i) $2.520$
(ii) $4.645$
(iii) $22.78$
(iv) $36.35$

A

$2.52$, $4.65$, $22.8$, $36.4$

B

$2.52$, $4.64$, $22.8$, $36.4$

C

$2.52$, $4.64$, $22.7$, $36.3$

D

$2.520$, $4.65$, $22.8$, $36.3$

Question 45: Palette 45/89

Objective Physics Vol-1 MCQ

Concept: The volume of a cylinder is given by the formula $V = \pi r^2 h$. In multiplication of measured quantities, the final result must contain only as many significant figures as present in the measurement with the least number of significant figures.

The length and the radius of a cylinder measured with slide callipers are found to be $4.54\text{ cm}$ and $1.75\text{ cm}$, respectively. Calculate the volume of the cylinder up to appropriate significant figures.

A

$43.66\text{ cm}^3$

B

$43.6\text{ cm}^3$

C

$43.58\text{ cm}^3$

D

$44.0\text{ cm}^3$

Question 46: Palette 46/89

Objective Physics Vol-1 MCQ

Concept: In any numerical measurement:
1. Zeros to the left of the first non-zero digit are leading zeros and are not significant.
2. Trailing zeros after a decimal point are significant.
3. The exponential factor ($10^3$) in scientific notation does not affect the number of significant figures.

What is the number of significant figures in $0.0310 \times 10^3$?

A

2

B

3

C

4

D

6

Question 47: Palette 47/89

Objective Physics Vol-1 MCQ

Concept: In scientific notation, the numerical value multiplied by a power of 10 contains the significant figures. All non-zero digits present in the coefficient are significant, while the exponential term ($10^{-6}$) represents the order of magnitude and does not affect the count of significant figures.

The number of significant figures in $11.118 \times 10^{-6}\text{ V}$ is

A

3

B

4

C

5

D

6

Question 48: Palette 48/89

Objective Physics Vol-1 MCQ

Concept: 1. Zeros between two non-zero digits are always significant (trapped zeros).
2. Leading zeros (zeros to the left of the first non-zero digit) are never significant.
3. Trailing zeros in a number without a decimal point are not significant.

In which of the following numerical values, all zeros are significant?

A

$0.2020$

B

$20.2$

C

$2020$

D

None of these

Question 49: Palette 49/89

Objective Physics Vol-1 MCQ

Concept: When adding numbers, the result is rounded off to the least number of decimal places present in any of the addends. After determining the sum, the rules for significant figures apply: trailing zeros after a decimal point are significant, while the exponential power of $10$ does not affect the count of significant figures.

What is the number of significant figures in $(3.20 + 4.80) \times 10^5$?

A

5

B

4

C

3

D

2

Question 50: Palette 50/89

Objective Physics Vol-1 MCQ

Concept: In addition and subtraction of measured values, the final result must be rounded off to the same number of decimal places as present in the measurement with the least number of decimal places.

Subtract $0.2\text{ J}$ from $7.26\text{ J}$ and express the result with correct number of significant figures.

A

$7.1\text{ J}$

B

$7.06\text{ J}$

C

$7.0\text{ J}$

D

None of these

Question 51: Palette 51/89

Objective Physics Vol-1 MCQ

Concept: In multiplication and division, the final result must contain only as many significant figures as are present in the measurement with the least number of significant figures.

Multiply $107.88$ by $0.610$ and express the result with correct number of significant figures.

A

$65.8068$

B

$64.807$

C

$65.81$

D

$65.8$

Question 52: Palette 52/89

Objective Physics Vol-1 MCQ

Concept: Volume is calculated as $\text{Volume} = \text{length} \times \text{breadth} \times \text{thickness}$. When multiplying measured values, all quantities must be converted to the same unit, and the final result must be rounded off to the same number of significant figures as the measurement with the least number of significant figures.

The length, breadth and thickness of rectangular sheet of metal are $4.234\text{ m}$, $1.005\text{ m}$ and $2.01\text{ cm}$, respectively. The volume of the sheet upto correct significant figures is

A

$0.0855\text{ m}^3$

B

$0.086\text{ m}^3$

C

$0.08556\text{ m}^3$

D

$0.085\text{ m}^3$

Question 53: Palette 53/89

Objective Physics Vol-1 MCQ

Concept: The area of cross-section of a circular wire is given by $A = \pi r^2$. When multiplying or squaring measured values, the final result must be rounded off to the same number of significant figures as the measurement with the least number of significant figures.

The radius of a thin wire is $0.16\text{ mm}$. The area of cross-section of the wire (in $\text{mm}^2$) with correct number of significant figures is

A

$0.08\text{ mm}^2$

B

$0.080\text{ mm}^2$

C

$0.0804\text{ mm}^2$

D

$0.080384\text{ mm}^2$

Question 54: Palette 54/89

Objective Physics Vol-1 MCQ

Concept: In multiplication and division of measured values, the final result must be rounded off to have as many significant figures as are present in the measurement with the least number of significant figures.

When $97.52$ is divided by $2.54$, the correct result (considering significant figures) is

A

$38.3937$

B

$38.394$

C

$65.81$

D

$38.4$

Question 55: Palette 55/89

Objective Physics Vol-1 MCQ

Concept: To find the order of magnitude of a physical quantity, express it in scientific notation as $a \times 10^b$, where $1 \le a < 10$ or $0.5 \le a < 5$ depending on the convention. Standard rule for order of magnitude states that if $a \le 3.16$ ($\sqrt{10}$), then $a$ is rounded to $10^0$ and the order of magnitude is $b$. If $a > 3.16$, then $a$ is rounded to $10^1$ and the order of magnitude becomes $b + 1$.

What is the order of magnitude of $[(5.0 \times 10^{-6}) \times (5.0 \times 10^{-9})]$ with due regards to significant digits?

A

$-14$

B

$-15$

C

$+15$

D

$+1$

Question 56: Palette 56/89

Objective Physics Vol-1 MCQ

Concept: The Least Count (LC) of a vernier callipers is the difference between the length of one Main Scale Division (MSD) and one Vernier Scale Division (VSD):
$\text{LC} = 1\text{ MSD} - 1\text{ VSD}$
Alternatively, it can be calculated using the relation:
$\text{LC} = \frac{\text{Value of 1 MSD}}{\text{Total number of divisions on vernier scale}}$

In a vernier callipers, 1 main scale division is $1\text{ mm}$ and the 9th main scale division coincides with the 10th vernier scale division. Find the least count of the vernier callipers.

A

$0.01\text{ mm}$

B

$0.1\text{ mm}$

C

$0.05\text{ mm}$

D

$0.2\text{ mm}$

Question 57: Palette 57/89

Objective Physics Vol-1 MCQ

Concept: 1. The average or mean length ($x_{\text{mean}}$) is the arithmetic mean of all measured values.
2. The absolute error in each measurement is $\vert{}\Delta x_i\vert{} = \vert{}x_i - x_{\text{mean}}\vert{}$.
3. The mean absolute error ($\Delta x_{\text{mean}}$) is the average of the absolute errors.
4. The percentage error ($\delta x$) is calculated as $\frac{\Delta x_{\text{mean}}}{x_{\text{mean}}} \times 100\%$.

The length of a rod as measured in an experiment is found to be $2.48\text{ m}$, $2.46\text{ m}$, $2.49\text{ m}$, $2.49\text{ m}$ and $2.46\text{ m}$. Find the average length and the percentage error.

A

$2.48\text{ m}$, $0.40\%$

B

$2.46\text{ m}$, $0.50\%$

C

$2.48\text{ m}$, $0.80\%$

D

$2.50\text{ m}$, $0.40\%$

Question 58: Palette 58/89

Objective Physics Vol-1 MCQ

Concept: 1. Mean value ($a_m$) is the arithmetic mean of all measurements.
2. Absolute error ($\Delta a_i$) in each measurement is the difference between the measured value and the mean value: $\Delta a_i = a_i - a_m$.
3. Mean absolute error ($\Delta a_{\text{mean}}$) is the arithmetic mean of the magnitudes of absolute errors: $\Delta a_{\text{mean}} = \frac{1}{n}\sum \vert{}\Delta a_i\vert{}$.

The diameter of a wire as measured by a screw gauge was found to be $2.620\text{ cm}$, $2.625\text{ cm}$, $2.630\text{ cm}$, $2.628\text{ cm}$ and $2.626\text{ cm}$. Find:
(i) mean value of diameter,
(ii) absolute error in each measurement, and
(iii) mean absolute error.

A

$2.626\text{ cm}$; $0.006\text{ cm}, 0.001\text{ cm}, -0.004\text{ cm}, -0.002\text{ cm}, 0.000\text{ cm}$; $0.003\text{ cm}$

B

$2.626\text{ cm}$; $-0.006\text{ cm}, -0.001\text{ cm}, +0.004\text{ cm}, +0.002\text{ cm}, 0.000\text{ cm}$; $0.003\text{ cm}$

C

$2.625\text{ cm}$; $-0.005\text{ cm}, 0.000\text{ cm}, +0.005\text{ cm}, +0.003\text{ cm}, +0.001\text{ cm}$; $0.005\text{ cm}$

D

$2.626\text{ cm}$; $-0.006\text{ cm}, -0.001\text{ cm}, +0.004\text{ cm}, +0.002\text{ cm}, 0.000\text{ cm}$; $0.010\text{ cm}$

Question 59: Palette 59/89

Objective Physics Vol-1 MCQ

Concept: 1. Fractional error $= \frac{\Delta a_{\text{mean}}}{a_m}$.
2. Percentage error $= \frac{\Delta a_{\text{mean}}}{a_m} \times 100\%$.
3. Expressing the result: Measured quantity $= a_m \pm \text{Percentage error}$.

For a measured diameter of a wire with mean value $2.626\text{ cm}$ and mean absolute error $0.003\text{ cm}$, calculate:
(iv) fractional error,
(v) percentage error, and
(vi) express the final result in terms of percentage error.

A

$0.0011$; $0.11\%$; $(2.626 \pm 0.11\%)\text{ cm}$

B

$0.003$; $0.30\%$; $(2.626 \pm 0.30\%)\text{ cm}$

C

$0.0011$; $1.1\%$; $(2.626 \pm 1.1\%)\text{ cm}$

D

$0.011$; $0.11\%$; $(2.626 \pm 0.003)\text{ cm}$

Question 60: Palette 60/89

Objective Physics Vol-1 MCQ

Concept: 1. Mean value ($n_{\text{mean}}$) is the arithmetic mean of all measured values.
2. Absolute error ($\Delta n_i$) in each measurement is calculated as $\Delta n_i = n_i - n_{\text{mean}}$.
3. Mean absolute error ($\Delta n_{\text{mean}}$) is the arithmetic mean of the magnitudes of the absolute errors.

The refractive index ($n$) of glass is found to have the values $1.49$, $1.50$, $1.52$, $1.54$ and $1.48$. Calculate:
(i) the mean value of refractive index,
(ii) absolute error in each measurement, and
(iii) mean absolute error.

A

$1.51$; $-0.02, -0.01, +0.01, +0.03, -0.03$; $0.02$

B

$1.51$; $+0.02, +0.01, -0.01, -0.03, +0.03$; $0.02$

C

$1.50$; $-0.01, 0.00, +0.02, +0.04, -0.02$; $0.03$

D

$1.51$; $-0.02, -0.01, +0.01, +0.03, -0.03$; $0.05$

Question 61: Palette 61/89

Objective Physics Vol-1 MCQ

Concept: 1. Fractional error $= \frac{\Delta n_{\text{mean}}}{n_{\text{mean}}}$.
2. Percentage error $= \frac{\Delta n_{\text{mean}}}{n_{\text{mean}}} \times 100\%$.
3. Expressing the result: Measured quantity $= n_{\text{mean}} \pm \text{Percentage error}$.

For a measured refractive index of glass with mean value $1.51$ and mean absolute error $0.02$, calculate:
(iv) fractional error,
(v) percentage error, and
(vi) express the final result in terms of percentage error.

A

$0.013$; $1.3\%$; $1.51 \pm 1.3\%$

B

$0.020$; $2.0\%$; $1.51 \pm 2.0\%$

C

$0.013$; $0.13\%$; $1.51 \pm 0.13\%$

D

$0.130$; $1.3\%$; $1.51 \pm 0.02$

Question 62: Palette 62/89

Objective Physics Vol-1 MCQ

Concept: In the addition or subtraction of two physical quantities, the absolute error in the final result is equal to the sum of the absolute errors in the individual quantities.
If $Z = A + B$ or $Z = A - B$, then $\Delta Z = \pm (\Delta A + \Delta B)$.

The volumes of two bodies are measured to be $V_1 = (10.2 \pm 0.02)\text{ cm}^3$ and $V_2 = (6.4 \pm 0.01)\text{ cm}^3$. Calculate the sum and difference in volumes with error limits.

A

$(16.6 \pm 0.03)\text{ cm}^3$ and $(3.8 \pm 0.03)\text{ cm}^3$

B

$(16.6 \pm 0.01)\text{ cm}^3$ and $(3.8 \pm 0.01)\text{ cm}^3$

C

$(16.6 \pm 0.03)\text{ cm}^3$ and $(3.8 \pm 0.01)\text{ cm}^3$

D

$(16.6 \pm 0.02)\text{ cm}^3$ and $(3.8 \pm 0.02)\text{ cm}^3$

Question 63: Palette 63/89

Objective Physics Vol-1 MCQ

Concept: 1. The mirror formula relates focal length ($f$), object distance ($u$), and image distance ($v$):
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \implies f = \frac{uv}{u + v}$
2. To find the error in focal length ($\Delta f$), differentiate the mirror formula:
$\frac{\Delta f}{f^2} = \frac{\Delta u}{u^2} + \frac{\Delta v}{v^2} \implies \Delta f = f^2 \left(\frac{\Delta u}{u^2} + \frac{\Delta v}{v^2}\right)$

Calculate the focal length of a spherical mirror from the following observations: Object distance $u = (50.1 \pm 0.5)\text{ cm}$ and image distance $v = (20.1 \pm 0.2)\text{ cm}$. Express the focal length with error limits.

A

$(14.3 \pm 0.15)\text{ cm}$

B

$(14.3 \pm 0.05)\text{ cm}$

C

$(14.3 \pm 0.25)\text{ cm}$

D

$(14.3 \pm 0.50)\text{ cm}$

Question 64: Palette 64/89

Objective Physics Vol-1 MCQ

Concept: 1. The surface area of a sphere is given by $S = 4\pi r^2$.
2. For a quantity $S = k r^n$ where $k$ is a constant, the fractional error is given by $\frac{\Delta S}{S} = n \left(\frac{\Delta r}{r}\right)$, which leads to the absolute error $\Delta S = 2 \left(\frac{\Delta r}{r}\right) S$.

The radius of a sphere is measured to be $(2.1 \pm 0.5)\text{ cm}$. Calculate its surface area with error limits.

A

$(55.4 \pm 26.4)\text{ cm}^2$

B

$(55.4 \pm 13.2)\text{ cm}^2$

C

$(55.4 \pm 5.2)\text{ cm}^2$

D

$(27.7 \pm 26.4)\text{ cm}^2$

Question 65: Palette 65/89

Objective Physics Vol-1 MCQ

Concept: Volume is calculated using the formula $V = \frac{m}{\rho}$, where $m$ is mass and $\rho$ is density. For quantities related by division, the maximum relative error in the calculated quantity is the sum of the relative errors in the individual measurements:
$\frac{\Delta V}{V} = \frac{\Delta m}{m} + \frac{\Delta \rho}{\rho}$

The mass and density of a solid sphere are measured to be $(12.4 \pm 0.1)\text{ kg}$ and $(4.6 \pm 0.2)\text{ kg m}^{-3}$ respectively. Calculate the volume of the sphere with error limits.

A

$(2.7 \pm 0.05)\text{ m}^3$

B

$(2.7 \pm 0.14)\text{ m}^3$

C

$(2.7 \pm 0.28)\text{ m}^3$

D

$(2.7 \pm 0.50)\text{ m}^3$

Question 66: Palette 66/89

Objective Physics Vol-1 MCQ

Concept: For small fractional changes, the percentage change in a physical quantity $X = k L^n$ (where $k$ and $n$ are constants) is related to the percentage change in length $L$ by:
$\frac{\Delta X}{X} \times 100\% = n \left(\frac{\Delta L}{L} \times 100\%\right)$

A thin copper wire of length $L$ increases in length by $2\%$ when heated from $T_1$ to $T_2$. If a copper cube having side $10L$ is heated from $T_1$ to $T_2$, what will be the percentage change in:
(i) area of one face of the cube, and
(ii) volume of the cube?

A

$2\%$ and $4\%$

B

$4\%$ and $6\%$

C

$4\%$ and $8\%$

D

$6\%$ and $6\%$

Question 67: Palette 67/89

Objective Physics Vol-1 MCQ

Concept: For a physical quantity $T = k l^a g^b$, where $k$ is a constant, the maximum percentage error in $T$ is given by the sum of the absolute power-weighted percentage errors of the individual variables:
$\frac{\Delta T}{T} \times 100\% = \vert{}a\vert{} \left(\frac{\Delta l}{l} \times 100\%\right) + \vert{}b\vert{} \left(\frac{\Delta g}{g} \times 100\%\right)$

Calculate the percentage error in the determination of the time period of a simple pendulum given by $T = 2\pi \sqrt{\frac{l}{g}}$, where $l$ and $g$ are measured with $\pm 1\%$ and $\pm 2\%$ errors, respectively.

A

$3\%$

B

$1.5\%$

C

$2\%$

D

$0.5\%$

Question 68: Palette 68/89

Objective Physics Vol-1 MCQ

Concept: For a physical quantity $Z = \frac{A^a B^b}{C^c D^d}$, the maximum relative percentage error is given by:
$\frac{\Delta Z}{Z} \times 100\% = a \left(\frac{\Delta A}{A} \times 100\%\right) + b \left(\frac{\Delta B}{B} \times 100\%\right) + c \left(\frac{\Delta C}{C} \times 100\%\right) + d \left(\frac{\Delta D}{D} \times 100\%\right)$
The relative error is the fractional value obtained by dividing the percentage error by $100$: $\frac{\Delta Z}{Z} = \frac{\text{Percentage Error}}{100}$.

Find the relative error in $Z$, if $Z = \frac{A^4 B^{1/3}}{C D^{3/2}}$ and the percentage error in the measurements of $A$, $B$, $C$ and $D$ are $4\%$, $2\%$, $3\%$ and $1\%$, respectively.

A

$0.2116$

B

$0.1621$

C

$21.16$

D

$0.02116$

Question 69: Palette 69/89

Objective Physics Vol-1 MCQ

Concept: The Least Count (LC) of a spherometer is calculated using the formula:
$\text{Least Count} = \frac{\text{Pitch}}{\text{Total number of divisions on the circular scale}}$
where Pitch is the distance moved by the spindle on the main scale for one complete rotation of the disc.

A spherometer has 100 equal divisions marked along the periphery of its disc and one full rotation of the disc advances on the main scale by $0.01\text{ cm}$. The least count of this system is

A

$10^{-2}\text{ cm}$

B

$10^{-4}\text{ cm}$

C

$10^{-5}\text{ cm}$

D

$10^{-1}\text{ cm}$

Question 70: Palette 70/89

Objective Physics Vol-1 MCQ

Concept: When calculating the arithmetic mean of measured values, the final result should be rounded off to the same number of decimal places as the measurement with the least number of decimal places (or reported according to standard rules of significant figures in addition/division).

Three measurements are made as $18.425\text{ cm}$, $7.21\text{ cm}$ and $5.0\text{ cm}$. The mean of measurements should be written as

A

$10.212\text{ cm}$

B

$10.21\text{ cm}$

C

$10.22\text{ cm}$

D

$10.2\text{ cm}$

Question 71: Palette 71/89

Objective Physics Vol-1 MCQ

Concept: The radius $r$ of a circle is related to its diameter $D$ by the linear relation:
$r = \frac{D}{2}$
Since $2$ is an exact constant without any measurement uncertainty, the fractional or percentage error in the radius is identical to the percentage error in the diameter:
$\frac{\Delta r}{r} \times 100\% = \frac{\Delta D}{D} \times 100\%$

If error in measuring diameter of a circle is $4\%$, the error in measuring radius of the circle would be

A

$2\%$

B

$8\%$

C

$4\%$

D

$1\%$

Question 72: Palette 72/89

Objective Physics Vol-1 MCQ

Concept: When two identical or different measured quantities are added together, the total magnitude is the sum of their individual values, and the absolute error in the result is the sum of the absolute errors of each individual measurement:
$L_{\text{net}} = L_1 + L_2$
$\Delta L_{\text{net}} = \pm (\Delta L_1 + \Delta L_2)$

The length of a rod is $(11.05 \pm 0.2)\text{ cm}$. What is the net length of the system of rods, when these two rods are joined side by side?

A

$(22.1 \pm 0.05)\text{ cm}$

B

$(22.1 \pm 0.4)\text{ cm}$

C

$(22.10 \pm 0.05)\text{ cm}$

D

$(22.1 \pm 0.1)\text{ cm}$

Question 73: Palette 73/89

Objective Physics Vol-1 MCQ

Concept: 1. Velocity is calculated as $v = \frac{s}{t}$, where $s$ is distance and $t$ is time.
2. For division, the relative error in velocity is the sum of the relative errors in distance and time:
$\frac{\Delta v}{v} = \frac{\Delta s}{s} + \frac{\Delta t}{t}$
3. The absolute error is given by $\Delta v = v \left(\frac{\Delta s}{s} + \frac{\Delta t}{t}\right)$.

A body travels uniformly a distance of $(13.8 \pm 0.2)\text{ m}$ in a time $(4.0 \pm 0.3)\text{ s}$. The velocity of the body within error limit is

A

$(3.45 \pm 0.2)\text{ ms}^{-1}$

B

$(3.45 \pm 0.5)\text{ ms}^{-1}$

C

$(3.45 \pm 0.4)\text{ ms}^{-1}$

D

$(3.45 \pm 0.3)\text{ ms}^{-1}$

Question 74: Palette 74/89

Objective Physics Vol-1 MCQ

Concept: For a physical quantity $V = k l^n$ (where $k$ is a constant and $n$ is a power), the relative percentage error in $V$ is related to the relative percentage error in $l$ by:
$\frac{\Delta V}{V} \times 100\% = n \left(\frac{\Delta L}{l} \times 100\%\right)$

A cuboid has volume $V = l \times 2l \times 3l$, where $l$ is the length of one side. If the relative percentage error in the measurement of $l$ is $1\%$, then the relative percentage error in measurement of $V$ is

A

$18\%$

B

$6\%$

C

$3\%$

D

$1\%$

Question 75: Palette 75/89

Objective Physics Vol-1 MCQ

Concept: 1. Pressure is defined as force per unit area: $P = \frac{F}{A} = \frac{F}{L^2}$.
2. The maximum fractional or percentage error in a calculated quantity $P = F L^{-2}$ is given by the sum of the percentage errors:
$\frac{\Delta P}{P} \times 100\% = \frac{\Delta F}{F} \times 100\% + 2 \left(\frac{\Delta L}{L} \times 100\%\right)$

A force $F$ is applied on a square plate of side $L$. If the percentage error in the determination of $L$ is $2\%$ and that in $F$ is $4\%$, what is the permissible error in pressure?

A

$8\%$

B

$6\%$

C

$4\%$

D

$2\%$

Question 76: Palette 76/89

Objective Physics Vol-1 MCQ

Concept: Joule's law of heating states that heat generated is $H = I^2 R t$. For a quantity given by $H = I^a R^b t^c$, the maximum relative percentage error is calculated as the sum of the absolute power-weighted percentage errors:
$\frac{\Delta H}{H} \times 100\% = 2 \left(\frac{\Delta I}{I} \times 100\%\right) + 1 \left(\frac{\Delta R}{R} \times 100\%\right) + 1 \left(\frac{\Delta t}{t} \times 100\%\right)$

The heat generated in a wire depends directly on the resistance, current and time. If the error in measuring the above are $1\%$, $2\%$ and $1\%$, respectively. The maximum error in measuring the heat is

A

$8\%$

B

$6\%$

C

$18\%$

D

$12\%$

Question 77: Palette 77/89

Objective Physics Vol-1 MCQ

Concept: 1. Kinetic energy $K$ is related to momentum $p$ and mass $m$ by the formula:
$K = \frac{p^2}{2m}$
2. When the change in a variable is large (such as $100\%$), relative error formulas using differentiation do not apply. Instead, calculate the new value directly:
$p' = p + 100\% \text{ of } p = 2p$
3. Find the new kinetic energy $K'$ and compute the percentage increase:
$\text{Percentage Error} = \frac{K' - K}{K} \times 100\%$

If the error in the measurement of momentum of a particle is $(+100\%)$, then the error in the measurement of kinetic energy is

A

$100\%$

B

$200\%$

C

$300\%$

D

$400\%$

Question 78: Palette 78/89

Objective Physics Vol-1 MCQ

Concept: 1. The volume of a spherical ball is given by $V = \frac{4}{3}\pi r^3$.
2. For a quantity $V = k r^n$ where $k$ is a constant, the relative percentage error is given by $\frac{\Delta V}{V} \times 100\% = n \left(\frac{\Delta r}{r} \times 100\%\right)$.

The radius of a ball is $(5.2 \pm 0.2)\text{ cm}$. The percentage error in the volume of the ball is (approximately)

A

$11\%$

B

$4\%$

C

$7\%$

D

$9\%$

Question 79: Palette 79/89

Objective Physics Vol-1 MCQ

Concept: For two resistors $R_1$ and $R_2$ connected in parallel, the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$, or $R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$.
The absolute error in parallel combination is calculated using:
$\Delta R_{eq} = R_{eq}^2 \left(\frac{\Delta R_1}{R_1^2} + \frac{\Delta R_2}{R_2^2}\right)$
The percentage error in equivalent resistance is $\frac{\Delta R_{eq}}{R_{eq}} \times 100\%$.

The values of two resistors are $(5.0 \pm 0.2)\text{ k}\Omega$ and $(10.0 \pm 0.1)\text{ k}\Omega$. What is the percentage error in the equivalent resistance when they are connected in parallel?

A

$2\%$

B

$5\%$

C

$7\%$

D

$3\%$

Question 80: Palette 80/89

Objective Physics Vol-1 MCQ

Concept: According to the principle of homogeneity of dimensions, physical quantities can be added or subtracted only if they have the same dimensions. Additionally, exponents in exponential functions must be dimensionless. Quantities with different dimensions can be multiplied or divided to form a new physical quantity.

If dimensions of $A$ and $B$ are different, then which of the following operation is valid?

A

$A / B$

B

$e^{-A/B}$

C

$A - B$

D

$A + B$

Question 81: Palette 81/89

Objective Physics Vol-1 MCQ

Concept: Significant figures reflect the precision of a measurement. Rules for determining significant figures:
1. All non-zero digits are significant.
2. Zeros preceding the first non-zero digit are leading zeros and are not significant.
3. Trailing zeros to the right of the decimal point in a measured quantity are significant.
4. Exponential factors ($10^n$) in scientific notation do not affect the number of significant figures.

The diameter of a wire is measured to be $0.0250 \times 10^{-4}\text{ m}$. The number of significant figures in the measurement is

A

five

B

four

C

three

D

nine

Question 82: Palette 82/89

Objective Physics Vol-1 MCQ

Concept: Electromotive force (emf) is defined as the work done per unit charge in moving a charge around a circuit, which is given by $V = W / q$. Electric potential is also defined as the work done per unit charge ($V = W / q$). Since both represent energy per unit charge, their dimensions are identical.

Dimensional formula for electromotive force is same as that for

A

potential

B

current

C

force

D

energy

Question 83: Palette 83/89

Objective Physics Vol-1 MCQ

Concept: Rules for determining significant figures:
1. All non-zero digits are significant.
2. Zeros preceding the first non-zero digit are leading zeros and are not significant.
3. Trailing zeros to the right of the decimal point are significant.

The number of significant figures in $0.06900$ is

A

5

B

4

C

2

D

3

Question 84: Palette 84/89

Objective Physics Vol-1 MCQ

Concept: When adding or subtracting decimal numbers, the result must be rounded off to the same number of decimal places as the quantity having the least number of decimal places (the least precise measurement).

The sum of the numbers $436.32$, $227.2$ and $0.301$ in appropriate significant figures is

A

$663.821$

B

$664$

C

$663.8$

D

$663.82$

Question 85: Palette 85/89

Objective Physics Vol-1 MCQ

Concept: Magnetic flux $\Phi$ is defined as the product of magnetic field $B$ and area $A$, given by $\Phi = B A \cos\theta$. Magnetic field $B$ can be derived from the Lorentz force equation $F = q v B$, which gives $B = F / (q v)$. Substituting $B$ into the flux formula and using base units gives the dimensional formula for magnetic flux as $[M L^2 T^{-2} A^{-1}]$.

The dimensional formula for magnetic flux is

A

$[M L^2 T^{-2} A^{-1}]$

B

$[M L^3 T^{-2} A^{-2}]$

C

$[M^0 L^{-2} T^{-2} A^{-2}]$

D

$[M L^2 T^{-1} A^2]$

Question 86: Palette 86/89

Objective Physics Vol-1 MCQ

Concept: The dimensional formula of a physical quantity shows how fundamental quantities like mass ($M$), length ($L$), and time ($T$) are combined to represent that quantity. By substituting the values of exponents $a$, $b$, and $c$, we can determine the dimensions of the quantity and compare them with standard physical quantities:
1. Force: $[M^1 L^1 T^{-2}]$
2. Pressure: $[M^1 L^{-1} T^{-2}]$
3. Velocity: $[M^0 L^1 T^{-1}]$
4. Acceleration: $[M^0 L^1 T^{-2}]$

If the dimensions of a physical quantity are given by $[M^a L^b T^c]$, then the physical quantity will be

A

force, if $a = 0, b = -1, c = -2$

B

pressure, if $a = 1, b = -1, c = -2$

C

velocity, if $a = 1, b = 0, c = -1$

D

acceleration, if $a = 1, b = 1, c = -2$

Question 87: Palette 87/89

Objective Physics Vol-1 MCQ

Concept: According to Coulomb's Law, the electrostatic force between two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by $F = \frac{k \cdot q_1 \cdot q_2}{r^2}$. Rearranging this equation to solve for the constant $k$ gives $k = \frac{F \cdot r^2}{q_1 \cdot q_2}$. Substituting the SI units for force ($\text{N}$), distance ($\text{m}$), and charge ($\text{C}$) yields the SI unit for $k$.

What is the units of $k = \frac{1}{4 \pi \varepsilon_0}$?

A

$\text{C}^2\text{N}^{-1}\text{m}^{-2}$

B

$\text{N-m}^2\text{C}^{-2}$

C

$\text{N-m}^2\text{C}^2$

D

Unitless

Question 88: Palette 88/89

Objective Physics Vol-1 MCQ

Concept: When multiplying or dividing physical quantities, the final result should retain as many significant figures as there are in the original measurement with the least number of significant figures.

The radius of a circle is $2.12\text{ m}$. Its area according to the rule of significant figures is

A

$14.1124\text{ m}^2$

B

$14.112\text{ m}^2$

C

$14.11\text{ m}^2$

D

$14.1\text{ m}^2$

Question 89: Palette 89/89

Objective Physics Vol-1 MCQ

Concept: According to Ohm's Law, potential difference is calculated as $V = I R$. When multiplying measured numbers, the final result must be rounded off to the same number of significant figures as the measurement with the fewest significant figures.

If the value of resistance is $10.845\ \Omega$ and the value of current is $3.23\text{ A}$, the value of potential with significant numbers would be

A

$35.0\text{ V}$

B

$3.50\text{ V}$

C

$35.029\text{ V}$

D

$35.03\text{ V}$