# A particle is moving along a circle of radius $$R$$ with constant speed $$v_0$$. What is the magnitude of change in velocity when the particle goes from point $$A$$ to $$B$$ as shown?                                   1. $$2{v}_0 \sin \frac{\theta}{2}$$ 2. $$v_0 \sin \frac{\theta}{2}$$ 3. $$2 v_0 \cos \frac{\theta}{2}$$ 4. $$v_0 \cos \frac{\theta}{2}$$

Subtopic:  Circular Motion |
78%
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Which of the following statements is incorrect?

 1 The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. 2 It is possible to have a situation $$\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0$$ but $$\frac{d\left|\overrightarrow{v}\right|}{dt}=0$$ 3 The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. 4 It is possible to have a situation in which $$\left|\frac{d\overrightarrow{v}}{dt}\right|=0$$ but $$\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0$$
Subtopic:  Acceleration |
63%
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A man is walking on a horizontal road with a speed of $$4$$ km/h. Suddenly, the rain starts vertically downwards with a speed of $$7$$ km/h. The magnitude of the relative velocity of the rain with respect to the man is:
1. $$\sqrt{33}$$
km/h
2. $$\sqrt{65}$$ km/h
3. $$8$$ km/h
4. $$4$$ km/h

Subtopic:  Relative Motion |
88%
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If a body is accelerating, then:

 1 it must speed up. 2 it may move at the same speed. 3 it may move with the same velocity. 4 it must slow down.
Subtopic:  Acceleration |
58%
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A shell is fired vertically upward with a velocity of $$20$$ m/s from a trolley moving horizontally with a velocity of $$10$$ m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: ($$g= 10~\text{m/s}^2$$${}^{}$)

 1 $$20$$ m 2 $$10$$ m 3 $$40$$ m 4 $$400$$ m
Subtopic:  Projectile Motion |
74%
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An object of mass m is projected from the ground with a momentum $$p$$ at such an angle that its maximum height is $$\frac{1}{4}$$th of its horizontal range. Its minimum kinetic energy in its path will be:

 1 $$\frac{p^2}{8 m}$$ 2 $$\frac{p^2}{4 m}$$ 3 $$\frac{3 p^2}{4 m}$$ 4 $$\frac{p^2}{m}$$
Subtopic:  Projectile Motion |
69%
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A particle moving on a curved path possesses a velocity of $$3$$ m/s towards the north at an instant. After $$10$$ s, it is moving with speed $$4$$ m/s towards the west. The average acceleration of the particle is:

 1 $$0.25~\text{m/s}^2,$$ $$37^{\circ}$$ south to east. 2 $$0.25~\text{m/s}^2,$$ $$37^{\circ}$$ west to north. 3 $$0.5~\text{m/s}^2,$$ $$37^{\circ}$$ east to north. 4 $$0.5~\text{m/s}^2,$$ $$37^{\circ}$$ south to west.

Subtopic:  Acceleration |
69%
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A man can row a boat with a speed of $$10$$ kmph in still water. The river flows at $$6$$ kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width $$1$$ km is:
1. $$\frac{1}{8}~\text{h}$$
2. $$\frac{1}{4}~\text{h}$$
3. $$\frac{1}{2}~\text{h}$$
4. $$1~\text{h}$$

Subtopic:  Relative Motion |
72%
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A bus is going to the North at a speed of $$30$$ kmph. It makes a $$90^{\circ}$$ left turn without changing the speed. The change in the velocity of the bus is:

 1 $$30$$ kmph towards $$W$$ 2 $$30$$ kmph towards $$S\text-W$$ 3 $$42.4$$ kmph towards $$S\text-W$$ 4 $$42.4$$ kmph towards $$N\text-W$$
Subtopic:  Speed & Velocity |
58%
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Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)

 1 The faster one 2 The slower one 3 Depends on masses 4 Both will reach simultaneously
Subtopic:  Projectile Motion |
76%
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