Q. No.| 1. | \(4\sqrt2~\text{ms}^{-1},45^\circ\) | 2. | \(4\sqrt2~\text{ms}^{-1},60^\circ\) |
| 3. | \(3\sqrt2~\text{ms}^{-1},30^\circ\) | 4. | \(3\sqrt2~\text{ms}^{-1},45^\circ\) |
The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:
| 1. | \(5\hat{i}~\text{m/s}^2\) | 2. | \(-4\hat{i}~\text{m/s}^2\) |
| 3. | \(-8\hat{j}~\text{m/s}^2\) | 4. | \(0\) |
| 1. | \(20\) | 2. | \(10\sqrt3\) |
| 3. | zero | 4. | \(10\) |
| 1. | \(3000~\text{m}\) | 2. | \(2800~\text{m}\) |
| 3. | \(2000~\text{m}\) | 4. | \(1000~\text{m}\) |
| 1. | \(5\) m | 2. | \(10\) m |
| 3. | \(20\) m | 4. | \(25\) m |
| 1. | \(10~\text{m/s}\) | 2. | zero |
| 3. | \(5\sqrt{3}~\text{m/s}\) | 4. | \(5~\text{m/s}\) |
A car starts from rest and accelerates at \(5~\text{m/s}^{2}.\) At \(t=4~\text{s}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(t=6~\text{s}?\)
(Take \(g=10~\text{m/s}^2\))
| 1. | \(20\sqrt{2}~\text{m/s}, 0~\text{m/s}^2\) | 2. | \(20\sqrt{2}~\text{m/s}, 10~\text{m/s}^2\) |
| 3. | \(20~\text{m/s}, 5~\text{m/s}^2\) | 4. | \(20~\text{m/s}, 0~\text{m/s}^2\) |
| 1. | \( \theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\) | 2. | \(\theta=\sin ^{-1}\left(\frac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) |
| 3. | \(\theta=\cos ^{-1}\left(\frac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) | 4. | \(\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |
A projectile is fired from the surface of the earth with a velocity of \(5~\text{m/s}\) and at an angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3~\text{m/s}\) at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is:
(given \(g=9.8~\text{m/s}^2\) )
| 1. | \(3.5~\text{m/s}^2\) | 2. | \(5.9~\text{m/s}^2\) |
| 3. | \(16.3~\text{m/s}^2\) | 4. | \(110.8~\text{m/s}^2\) |
The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the 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. | \(-2\hat i-3\hat j~\) |
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