# A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip(returning to the initial point) is: (1) 5 min (2) 60 min (3) 20 min (4) 30 min

Subtopic:  Relative Motion |
54%
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A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south.

(1) 30° with downstream

(2) 60° with downstream

(3) 120° with downstream

(4) South

Subtopic:  Relative Motion |
54%
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A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is

(1) East-north direction

(2) West-north direction

(3) South-east direction

(4) None of these

Subtopic:  Relative Motion |
60%
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A ball P is dropped vertically and another ball Q is thrown horizontally from the  same height and at the same time. If air resistance is neglected, then

(1) Ball P reaches the ground first

(2) Ball Q reaches the ground first

(3) Both reach the ground at the same time

(4) The respective masses of the two balls will decide the time

Subtopic:  Projectile Motion |
81%
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A frictionless wire $$AB$$ is fixed on a sphere of radius $$R$$. A very small spherical ball slips on this wire. The time taken by this ball to slip from $$A$$ to $$B$$ is:

1. $$\frac{2 \sqrt{g R}}{g \cos \theta}$$
2. $$2 \sqrt{g R} . \frac{\cos \theta}{g}$$
3. $$2 \sqrt{\frac{R}{g}}$$
4. $$\frac{g R}{\sqrt{g\cos \theta}}$$

Subtopic:  Uniformly Accelerated Motion |
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From NCERT
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A body is slipping from an inclined plane of height $$h$$ and length $$l$$. If the angle of inclination is $$\theta$$, the time taken by the body to come from the top to the bottom of this inclined plane is:
1. $$\sqrt{\frac{2 h}{g}}$$
2. $$\sqrt{\frac{2 l}{g}}$$
3. $$\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}$$
4. $$\sin \theta \sqrt{\frac{2 h}{g}}$$

Subtopic:  Uniformly Accelerated Motion |
59%
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An aeroplane is moving with a velocity $$u$$. It drops a packet from a height $$h$$. The time $$t$$ taken by the packet to reach the ground will be:
1. $$\sqrt{\left(\frac{2 g}{h}\right)}$$
2. $$\sqrt{\left(\frac{2 u}{g}\right)}$$
3. $$\sqrt{\left(\frac{h}{2 g}\right)}$$
4. $$\sqrt{\left(\frac{2 h}{g}\right)}$$

Subtopic:  Projectile Motion |
83%
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An aeroplane is moving with horizontal velocity u at height h. The velocity of a packet dropped from it on the earth's surface will be (g is acceleration due to gravity)

(1) $\sqrt{{u}^{2}+2gh}$

(2) $\sqrt{2gh}$

(3) 2 gh

(4) $\sqrt{{u}^{2}-2gh}$

Subtopic:  Projectile Motion |
58%
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A bullet is fired with a speed of $1000\text{\hspace{0.17em}\hspace{0.17em}}m/\mathrm{sec}$ in order to hit a target 100 m away. If $g=10\text{\hspace{0.17em}\hspace{0.17em}}m/{s}^{2}$, the gun should be aimed:

(1) Directly towards the target

(2) 5 cm above the target

(3) 10 cm above the target

(4) 15 cm above the target

Subtopic:  Projectile Motion |
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A body sliding on a smooth inclined plane requires $$4$$ seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top?

 1 $$1~\text{s}$$ 2 $$2~\text{s}$$ 3 $$4~\text{s}$$ 4 $$16~\text{s}$$
Subtopic:  Uniformly Accelerated Motion |
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