Unit 2 – Kinematics
I. Multiple Choice Questions

1. Which one of the following Cartesian coordinate systems is not followed in physics?

Cartesian coordinate systems
Answer: d

2. Identify the unit vector in the following.

(a) $\hat{i} + \hat{j}$
(b) $\dfrac{\hat{i}}{\sqrt{2}}$
(c) $\dfrac{\hat{k}-\hat{j}}{\sqrt{2}}$
(d) $\dfrac{\hat{i}+\hat{j}}{\sqrt{2}}$
Answer: d

3. Which one of the following physical quantities cannot be represented by a scalar?

(a) Mass
(b) Length
(c) Momentum
(d) Magnitude of acceleration
Answer: c

4. Two objects of masses $m_1$ and $m_2$ fall from heights $h_1$ and $h_2$ respectively. The ratio of the magnitude of their momentum when they hit the ground is

(a) $\sqrt{\dfrac{h_1}{h_2}}$
(b) $\sqrt{\dfrac{m_1 h_1}{m_2 h_2}}$
(c) $\dfrac{m_1}{m_2}\sqrt{\dfrac{h_1}{h_2}}$
(d) $\dfrac{m_1}{m_2}$
Answer: c

5. If a particle has negative velocity and negative acceleration, its speed

(a) increases
(b) decreases
(c) remains same
(d) zero
Answer: a

6. If the velocity is $\vec{v} = 2\hat{i} + t^2\hat{j} - 9\hat{k}$, then the magnitude of acceleration at $t = 0.5\,s$ is

(a) $1\;m\,s^{-2}$
(b) $2\;m\,s^{-2}$
(c) zero
(d) $-1\;m\,s^{-2}$
Answer: a

7. If an object is dropped from the top of a building and it reaches the ground at $t = 4\,s$, then the height of the building is (ignoring air resistance) $(g = 9.8\,m\,s^{-2})$

(a) $77.3\,m$
(b) $78.4\,m$
(c) $80.5\,m$
(d) $79.2\,m$
Answer: b

8. A ball is projected vertically upwards with velocity $v$. It comes back to ground in time $t$. Which $v$–$t$ graph shows the motion correctly?

Velocity time graphs
Answer: c

9. If one object is dropped vertically downward and another object is thrown horizontally from the same height, the ratio of vertical distance covered by both objects at any instant $t$ is

(a) 1
(b) 2
(c) 4
(d) 0.5
Answer: a

10. A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

Ball motion diagrams
Answer: a

11. If a particle executes uniform circular motion in the $xy$ plane in clockwise direction, then the angular velocity is in

(a) $+y$ direction
(b) $+z$ direction
(c) $-z$ direction
(d) $-x$ direction
Answer: c

12. If a particle executes uniform circular motion, choose the correct statement (NEET 2016)

(a) Velocity and speed are constant
(b) Acceleration and speed are constant
(c) Velocity and acceleration are constant
(d) Speed and magnitude of acceleration are constant
Answer: d

13. If an object is thrown vertically up with initial speed $u$ from the ground, the time taken to return back to ground is

(a) $\dfrac{u^2}{2g}$
(b) $\dfrac{u^2}{g}$
(c) $\dfrac{u}{2g}$
(d) $\dfrac{2u}{g}$
Answer: d

14. Two objects are projected at angles $30^\circ$ and $60^\circ$ respectively with respect to the horizontal. If their ranges are $R_{30^\circ}$ and $R_{60^\circ}$, choose the correct relation.

(a) $R_{30^\circ} = R_{60^\circ}$
(b) $R_{30^\circ} = 4R_{60^\circ}$
(c) $R_{30^\circ} = \dfrac{R_{60^\circ}}{2}$
(d) $R_{30^\circ} = 2R_{60^\circ}$
Answer: a

15. An object is dropped in an unknown planet from height $50\,m$, it reaches the ground in $2\,s$. The acceleration due to gravity in this unknown planet is

(a) $20\,m\,s^{-2}$
(b) $25\,m\,s^{-2}$
(c) $15\,m\,s^{-2}$
(d) $30\,m\,s^{-2}$
Answer: b