An aeroplane is moving with a velocity \(u\). It drops a packet from a height \(h\). The time \(t\) taken by the packet in reaching 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 |
 84%
From NCERT
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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 s 2. 2 s
3. 4 s 4. 16 s

Subtopic:  Uniformly Accelerated Motion |
 70%
From NCERT
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The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is 30°) is:

             

1. \(\frac{1}{2} \mathrm{sec} \) 2. \(2 ~\mathrm{sec} \)
3. \(4~ \mathrm{sec} \) 4. \(1~ \mathrm{sec} \)
Subtopic:  Uniformly Accelerated Motion |
 71%
From NCERT
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A particle moves with constant angular velocity in a circle. During the motion its:

1. Energy is conserved
2. Momentum is conserved
3. Energy and momentum both are conserved
4. None of the above is conserved

Subtopic:  Circular Motion |
From NCERT
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What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :

1. \(6 \hat{i}+2 \hat{j}-3 \hat{k} \)           
2. \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \)
3. \(4 \hat{i}-13 \hat{j}+6 \hat{k}\)
4. \(6 \hat{i}-2 \hat{j}+8 \hat{k}\)

Subtopic:  Circular Motion |
 85%
From NCERT
PMT - 2000
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A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is:

1. 2 π v/T

2. 2 π r/T

3. 2 π r2/T

4. 2 π v2/T

Subtopic:  Circular Motion |
 62%
From NCERT
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If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where θ 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 |
 81%
From NCERT
AIIMS - 1998
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The coordinates of a moving particle at any time ‘t’ are given by x = αt3 and y = βt3. The speed of the particle at time ‘t’ is given by:

1. α2+β2

2. 3 tα2+β2

3. 3 t2α2+β2

4. t2α2+β2

Subtopic:  Speed & Velocity |
 78%
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 |
 85%
From NCERT
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Four bodies P, Q, R and S are projected with equal velocities having angles of projection 15o, 30o, 45o and 60o 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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