# If the equation for the displacement of a particle moving on a circular path is given by $$\theta = 2t^3 + 0.5$$ where $$\theta$$ is in radians and $$t$$ in seconds, then the angular velocity of the particle after $$2$$ sec from its start is: 1. $$8$$ rad/sec 2. $$12$$ rad/sec 3. $$24$$ rad/sec 4. $$36$$ rad/sec

Subtopic:  Circular Motion |
82%
From NCERT
AIIMS - 1998
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The coordinates of a moving particle at any time $$t$$ are given by $$x= \alpha t^3$$ and $$y = \beta t^3$$. The speed of the particle at time $$t$$ is given by:

 1 $$\sqrt{\alpha^{2} + \beta^{2}}$$ 2 $$3t \sqrt{\alpha^{2} + \beta^{2}}$$ 3 $$3t^{2} \sqrt{\alpha^{2} +\beta^{2}}$$ 4 $$t^{2} \sqrt{\alpha^{2} +\beta^{2}}$$
Subtopic:  Speed & Velocity |
79%
From NCERT
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At the top of the trajectory of a projectile, the directions of its velocity and acceleration are:
 1 perpendicular to each other. 2 parallel to each other. 3 inclined to each other at an angle of $$45^\circ$$. 4 antiparallel to each other.
Subtopic:  Projectile Motion |
84%
From NCERT
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Four bodies $$P$$, $$Q$$, $$R$$ and $$S$$ are projected with equal velocities having angles of projection $$15^{\circ},$$ $$30^{\circ},$$$$45^{\circ},$$ and $$60^{\circ}$$ with the horizontal respectively. The body having the shortest range is?

 1 $$P$$ 2 $$Q$$ 3 $$R$$ 4 $$S$$
Subtopic:  Projectile Motion |
74%
From NCERT
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A stone projected with a velocity $$u$$ at an angle $$\theta$$ with the horizontal reaches maximum height $$H_1$$. When it is projected with velocity $$u$$ at an angle $$\frac{\pi}{2}-\theta$$ with the horizontal, it reaches maximum height $$H_2$$. The relation between the horizontal range of the projectile $$R$$ and $$H_1$$ & $$H_2$$ is:

 1 $$R=4 \sqrt{H_1 H_2}$$ 2 $$R=4\left(H_1-H_2\right)$$ 3 $$R=4\left(H_1+H_2\right)$$ 4 $$R=\frac{H_1{ }^2}{H_2{ }^2}$$
Subtopic:  Projectile Motion |
83%
From NCERT
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A cricketer can throw a ball to a maximum horizontal distance of $$100~\text{m}$$. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is:
1. $$100~\text{m}$$
2. $$80~\text{m}$$
3. $$60~\text{m}$$
4. $$50~\text{m}$$

Subtopic:  Projectile Motion |
75%
From NCERT
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The horizontal range of a projectile is $$4 \sqrt{3}$$ times its maximum height. Its angle of projection will be:
1. $$45^{\circ}$$
2. $$60^{\circ}$$
3. $$90^{\circ}$$
4. $$30^{\circ}$$

Subtopic:  Projectile Motion |
74%
From NCERT
PMT - 2003
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A boat is moving with a velocity $$3\hat i + 4\hat j$$ with respect to ground. The water in the river is moving with a velocity$$-3\hat i - 4 \hat j$$ with respect to ground. The relative velocity of the boat with respect to water is:
1. $$8\hat j$$
2. $$-6\hat i-8\hat j$$
3. $$6\hat i+8\hat j$$
4. $$5\sqrt{2}$$

Subtopic:  Relative Motion |
83%
From NCERT
PMT - 1998
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A river is flowing from east to west at a speed of $$5$$ m/min. A man on south bank of river, capable of swimming $$10$$ m/min in still water, wants to swim across the river in shortest time. He should swim:

 1 Due north 2 Due north-east 3 Due north-east with double the speed of the river 4 None of the above
Subtopic:  Relative Motion |
58%
From NCERT
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A man sitting in a bus travelling in a direction from west to east with a speed of $$40$$ km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear:

 1 To fall vertically downwards 2 To fall at an angle going from west to east 3 To fall at an angle going from east to west 4 The information given is insufficient to decide the direction of the rain
Subtopic:  Relative Motion |
53%
From NCERT
PMT - 1999
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