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. \( \sqrt{\left(\frac{2 h}{g}\right)}\)
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 |
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 ) is:
1. | \(\frac{1}{2} \mathrm{sec} \) | 2. | \(2 ~\mathrm{sec} \) |
3. | \(4~ \mathrm{sec} \) | 4. | \(1~ \mathrm{sec} \) |
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 |
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. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
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.
3.
4.
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
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. | 2. | ||
3. | 4. |
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 |
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 |