Unit And Dimensions Set-1

Practice Important MCQs for Unit And Dimensions — Physics, Class JEE.

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Q1. The unit of impulse is the same as that of

(A)

Moment of force

(B)

Linear momentum

(C)

Rate of change of linear momentum

(D)

Force

Q2. Which of the following is not the unit of energy?

(A)

Watt-hour

(B)

Electron-volt

(C)

$N \times m$

(D)

$kg \times m/s$

Q3. If $a$ and $b$ are two physical quantities having different dimensions then which of the following can denote a new physical quantity?

(A)

$a + b$

(B)

$a - b$

(C)

$a/b$

(D)

$e^{ab}$

Q4. 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 $\alpha$

(A)

will be dimensionless

(B)

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

(C)

will have dimensions as that of $P$

(D)

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

Q5. Which pair of following quantities has dimensions different from each other?

(A)

Impulse and linear momentum

(B)

Planck's constant and angular momentum

(C)

Moment of inertia and moment of force

(D)

Young's modulus and pressure

Q6. The product of energy and time is called action. The dimensional formula for action is same as that for

(A)

Power

(B)

Angular energy

(C)

Force $\times$ velocity

(D)

Impulse $\times$ distance

Q7. What is the physical quantity whose dimensions are $[M L^2 T^{-2}]$ ?

(A)

Kinetic energy

(B)

Pressure

(C)

Momentum

(D)

Power

Q8. 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

(A)

Angle

(B)

Length

(C)

Mass

(D)

Time

Q9. 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.

(A)

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

(B)

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

(C)

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

(D)

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

Q10. 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

(A)

Velocity

(B)

Displacement

(C)

Acceleration

(D)

Momentum

Q11. 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

(A)

Wave velocity

(B)

Amplitude

(C)

Wavelength

(D)

Wave frequency

Q12. 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

(A)

$m/s$

(B)

$m/s^2$

(C)

meter

(D)

$/sec$

Q13. If the units of mass and length are doubled then the unit of kinetic energy will become

(A)

2 times

(B)

4 times

(C)

8 times

(D)

16 times

Q14. 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

(A)

16%

(B)

0.8%

(C)

1.8%

(D)

Q15. The dimensions of a cuboidal block measured with a vernier callipers having least count of 0.1 mm is 5 mm $\times$ 10 mm $\times$ 5 mm. The maximum percentage error in measurement of volume of the block is

(A)

(B)

10%

(C)

15%

(D)

20%

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