Unit And Dimensions Set-1

Question 1

The unit of impulse is the same as that of

Accepted Answer

Linear momentum

Answer

Moment of force

Answer

Rate of change of linear momentum

Answer

Force

Question 2

Which of the following is not the unit of energy?

Accepted Answer

$kg 	imes m/s$

Answer

Watt-hour

Answer

Electron-volt

Answer

$N 	imes m$

Question 3

If $a$ and $b$ are two physical quantities having different dimensions then which of the following can denote a new physical quantity?

Accepted Answer

$a/b$

Answer

$a + b$

Answer

$a - b$

Answer

$e^{ab}$

Question 4

The time dependence of a physical quantity $P = P_0 \exp(-\alpha t^2)$ where $\alpha$ is a constant and $t$ is time. The constant $\alpha$

Accepted Answer

will have dimensions of $T^{-2}$

Answer

will be dimensionless

Answer

will have dimensions as that of $P$

Answer

will have dimensions equal to the dimension of $P$ multiplied by $T^{-2}$

Question 5

Which pair of following quantities has dimensions different from each other?

Accepted Answer

Moment of inertia and moment of force

Answer

Impulse and linear momentum

Answer

Planck's constant and angular momentum

Answer

Young's modulus and pressure

Question 6

The product of energy and time is called action. The dimensional formula for action is same as that for

Accepted Answer

Impulse $	imes$ distance

Answer

Power

Answer

Angular energy

Answer

Force $	imes$ velocity

Question 7

What is the physical quantity whose dimensions are $[M L^2 T^{-2}]$?

Accepted Answer

Kinetic energy

Answer

Pressure

Answer

Momentum

Answer

Power

Question 8

If $E, M, J$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then $\frac{E J^2}{M^5 G^2}$ has the dimensions of

Accepted Answer

Angle

Answer

Length

Answer

Mass

Answer

Time

Question 9

The position of a particle at time $t$ is given by $x(t) = \frac{V_0}{\alpha} (1 - e^{-\alpha t})$ where $V_0$ is a constant and $\alpha > 0$. The dimensions of $V_0$ and $\alpha$ are respectively.

Accepted Answer

$M^0 L^1 T^{-1}$ and $T^{-1}$

Answer

$M^0 L^1 T^0$ and $T^{-1}$

Answer

$M^0 L^1 T^0$ and $T^{-2}$

Answer

$M^0 L^1 T^{-1}$ and $T^{-2}$

Question 10

If force $F$ is given by $F = P t^{-1} + \alpha t$, where $t$ is time. The unit of $P$ is same as that of

Accepted Answer

Momentum

Answer

Velocity

Answer

Displacement

Answer

Acceleration

Question 11

When a wave traverses a medium, the displacement of a particle located at $x$ at time $t$ is given by $y = a \sin(bt - cx)$ where $a, b$ and $c$ are constants of the wave. The dimensions of $b$ are the same as those of

Accepted Answer

Wave frequency

Answer

Wave velocity

Answer

Amplitude

Answer

Wavelength

Question 12

In a book, the answer for a particular question is expressed as $b = \frac{m a}{k} \left[ \sqrt{1 + \frac{2 k l}{m a}} \right]$ here $m$ represents mass, $a$ represents acceleration, $l$ represents length. The unit of $b$ should be

Accepted Answer

meter

Answer

$m/s$

Answer

$m/s^2$

Answer

$/sec$

Question 13

If the units of mass and length are doubled then the unit of kinetic energy will become

Accepted Answer

4 times

Answer

2 times

Answer

8 times

Answer

16 times

Question 14

The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The percentage error in the time period is

Accepted Answer

0.8%

Answer

16%

Answer

1.8%

Answer

8%

Question 15

The dimensions of a cuboidal block measured with a vernier callipers having least count of 0.1 mm is 5 mm $	imes$ 10 mm $	imes$ 5 mm. The maximum percentage error in measurement of volume of the block is

Accepted Answer

5%

Answer

10%

Answer

15%

Answer

20%

Question 16

In an experiment the quantities $x, y$ and $z$ are measured. Then $i$ is calculated from the data as $i = \frac{x^2 y}{z^2}$. If percentage errors in $x, y$ and $z$ are respectively 1%, 3%, 2%, then percentage error in $i$ is:

Accepted Answer

13%

Answer

10%

Answer

4%

Answer

7%

Question 17

The external and internal diameters of a hollow cylinder are measured to be $(4.23 \pm 0.01)$ cm and $(3.89 \pm 0.01)$ cm. The thickness of the wall of the cylinder is

Accepted Answer

$(0.34 \pm 0.02)$ cm

Answer

$(0.17 \pm 0.02)$ cm

Answer

$(0.17 \pm 0.01)$ cm

Answer

$(0.34 \pm 0.01)$ cm

Question 18

Two resistors $R_1 = (24 \pm 0.5)  \Omega$ and $R_2 = (8 \pm 0.3)  \Omega$ are joined in series. The equivalent resistance is

Accepted Answer

$32 \pm 0.8  \Omega$

Answer

$32 \pm 0.33  \Omega$

Answer

$32 \pm 0.2  \Omega$

Answer

$32 \pm 0.5  \Omega$

Question 19

The pitch of a screw gauge is 0.5 mm and there are 100 divisions on its circular scale. The instrument reads +2 divisions when nothing is put in-between its jaws. In measuring the diameter of a wire, there are 8 divisions on the main scale and 83rd division coincides with the reference line. Then the diameter of the wire is

Accepted Answer

4.405 mm

Answer

4.05 mm

Answer

3.05 mm

Answer

1.25 mm

Question 20

The smallest division on the main scale of a vernier callipers is 1 mm, and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a sphere, the zero mark of the vernier scale lies between 2.0 and 2.1 cm and the fifth division of the vernier scale coincides with a mark on main scale. Then diameter of the sphere is

Accepted Answer

2.05 cm

Answer

3.05 cm

Answer

2.50 cm

Answer

None of these

Question 21

For a satellite orbiting around the Earth, its orbital velocity $v_0$ is found to depend on mass of Earth $M$, radius of earth $R$ and universal gravitational constant $G$. The orbital velocity is proportional to

Accepted Answer

$G^{1/2} M^{1/2} R^{-1/2}$

Answer

$G^{-1} M^2 R^{-1}$

Answer

$G^2 M^2 R^{-1}$

Answer

None of these

Question 22

The vernier constant of a vernier callipers is 0.1 mm and it has zero error of $-0.05$ cm. While measuring the diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The correct diameter will be $n 	imes 10^{-2}$ cm. Find $n$

Accepted Answer

180

Answer

220

Answer

160

Answer

200

Question 23

In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10g and 0.1s respectively. The unit of force in this system will be equal to

Accepted Answer

1/10 N

Answer

1 N

Answer

10 N

Answer

100 N

Question 24

In sub-atomic physics, one often associates a characteristic wavelength $\lambda$ with a particle of mass $m$. If $\hbar = \frac{h}{2\pi}$ ($h$ being Planck's constant) and $c$ is the speed of light, which of the following expression is most likely to be correct one?

Accepted Answer

$\lambda = \frac{\hbar}{m c}$

Answer

$\lambda = \frac{\hbar c}{m}$

Answer

$\lambda = \frac{\hbar}{m c^2}$

Answer

$\lambda = \frac{m \hbar}{c}$

Question 25

If the mass, time and energy are taken as fundamental physical quantities then dimensional formula of length is

Accepted Answer

$[M^{-1/2} T^1 E^{1/2}]$

Answer

$[M^{1/2} T^1 E^{-1/2}]$

Answer

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

Answer

None of these

Question 26

Given that $\ln(\alpha / p \beta) = \alpha z / k_B 	heta$ where $p$ is pressure, $z$ is distance, $k_B$ is Boltzmann constant and $	heta$ is temperature. The dimensions of $\beta$ are

Accepted Answer

$L^2 M^0 T^0$

Answer

$L^0 M^0 T^0$

Answer

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

Answer

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

Question 27

Let $y = l^2 - \frac{l^3}{z}$ where $l = 2.0 \pm 0.1$, $z = 1.0 \pm 0.1$, then the value of $y$ is given by

Accepted Answer

$-4 \pm 1.6$

Answer

$-4 \pm 2.4$

Answer

$-4 \pm 0.8$

Answer

None of these

Question 28

The time periods of a pendulum are measured to be $T_1 = 8.01$ s and $T_2 = 8.41$ s by a student who used stop watch having least count = 0.01 sec, then the best reported measurement of time period (in sec) is

Accepted Answer

$8.2 \pm 0.2$

Answer

$8.41 \pm 0.2$

Answer

$8.21 \pm 0.01$

Answer

$8.41 \pm 0.01$

Question 29

A gas bubble from an explosion under water oscillates with period $T$ proportional to $p^a d^b E^c$, where $p$ is static pressure, $d$ is the density of water, $E$ is the total energy of the explosion. The values of $a, b, c$ respectively will be

Accepted Answer

$\frac{-5}{6}, \frac{1}{2}, \frac{1}{3}$

Answer

$\frac{1}{3}, \frac{1}{2}, \frac{-5}{6}$

Answer

$\frac{1}{3}, \frac{1}{2}, \frac{5}{6}$

Answer

$\frac{-5}{6}, \frac{1}{3}, \frac{1}{2}$

Question 30

Electric field in a certain region is given by $\vec{E} = \left( \frac{A}{x^2} + \frac{B}{y^2} \right)$. The SI unit of $A$ and $B$ are:

Accepted Answer

$Nm^2 C^{-1}; Nm^3 C^{-1}$

Answer

$Nm^3 C^{-1}; Nm^2 C^{-1}$

Answer

$Nm^3 C; Nm^2 C$

Answer

$Nm^2 C; Nm^3 C$

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