← Back to Physics-I

Dimensions & Error Analysis

91 Questions Start Objective Physics Vol-1 Test
All Exams Objective Physics Vol-1 DPT
Q1 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^0 L^1 T^{-2}]$
Q2 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^1 L^1 T^0 A^1]$
Q3 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^0 L^2 T^{-3} A^{-1}]$
Q4 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^0 L^{-2} T^4 A^1]$
Q5 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^{-1} L^2 T^{-3} A^{-2}]$
Q6 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^1 L^0 T^{-1} A^0]$
Q7 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q8 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[M^{-3} L^{-2} T^8 A^4]$
Q9 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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 $[b] = [M^0 L^1 T^1]$
Q10 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[a] = [L T^{-2}]$, $[b] = [L T^{-2}]$, $[c] = [L]$, $[d] = [T^{-1}]$
Q11 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$9 \times 10^7\text{ new units}$
Q12 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$6.67 \times 10^{-11}\text{ dyne}\cdot\text{cm}^2/\text{g}^2$
Q13 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$f = \frac{k}{l} \sqrt{\frac{\mu}{F}}$
Q14 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$F = \frac{m v}{r^2}$
Q15 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
In the SI system, the unit of temperature is
A.
degree centigrade
B.
kelvin
C.
degree celsius
D.
degree Fahrenheit
Q16 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q17 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q18 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q19 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$625$
Q20 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[\text{M L T}^{-2}]$
Q21 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q22 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q23 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q24 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q25 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[\text{M L}^{-1} \text{T}^{-1}]$
Q26 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[\text{M L}^3 \text{T}^{-1} \text{Q}^{-1}]$
Q27 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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 $[\text{M L T}^{-2}]$
Q28 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[\text{M L T}^{-1}]$
Q29 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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
Q30 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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 $p$
Q31 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[\text{M L}^3 \text{T}^{-1}]$
Q32 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$[\text{LT}]$
Q33 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$10^{-5}$
Q34 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$x = 1, y = 1, z = 1$
Q35 Objective Physics Vol-1 Dimensions Analysis MCQ
24 Jul 2026
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.
$v^6$
Q36 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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
Q37 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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
Q38 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$7.2022 \times 10^3\text{ cm}$
Q39 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$22.0\text{ cm}$
Q40 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$21.49\text{ W}$
Q41 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$0.1\text{ cm}^3$
Q42 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$4\text{ s}$
Q43 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$5.0\text{ g/cm}^3$
Q44 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$2.520$, $4.65$, $22.8$, $36.3$
Q45 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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.
$44.0\text{ cm}^3$
Q46 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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
Q47 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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
Q48 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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
Q49 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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
Q50 Objective Physics Vol-1 Significant Figures MCQ
24 Jul 2026
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