Question 1: Palette 1/89

Objective Physics Vol-1 MCQ

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$5.74\text{ g}$ 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$35.03\text{ V}$