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. | \(R=\frac{H_1{ }^2}{H_2{ }^2}\) |
A boat is moving with a velocity 3i + 4j with respect to ground. The water in the river is moving with a velocity – 3i – 4j with respect to ground. The relative velocity of the boat with respect to water is
1. 8j
2. – 6i – 8j
3. 6i +8j
4.
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. |
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. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
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. | \(1~ \mathrm{sec} \) |
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 particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant. Based on the information given, which of the following is true?
1. | Velocity and acceleration, both are parallel to r. |
2. | Velocity is perpendicular to r and acceleration is directed towards the origin. |
3. | Velocity is not perpendicular to r and acceleration is directed away from the origin. |
4. | Velocity and acceleration, both are perpendicular to r. |
Two men P & Q are standing at corners A & B of square ABCD of side 8 m. They start moving along the track with constant speed 2 m/s and 10 m/s respectively. The time when they will meet for the first time, is equal to:
1. 2 sec
2. 3 sec
3. 1 sec
4. 6 sec
The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:
1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |
3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |