A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is
1. 100 m
2. 80 m
3. 60 m
4. 50 m
The horizontal range of a projectile is times its maximum height. Its angle of projection will be:
1. 45°
2. 60°
3. 90°
4. 30°
A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H1. When it is projected with velocity u at an angle with the horizontal, it reaches maximum height H2. The relation between the horizontal range of the projectile R and H1 & H2 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. | \(R=\frac{H_1{ }^2}{H_2{ }^2}\) |
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 |
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 |
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. |
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
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.
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 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 |