Q. No.| 1. | \(3000~\text{m}\) | 2. | \(2800~\text{m}\) |
| 3. | \(2000~\text{m}\) | 4. | \(1000~\text{m}\) |
1. \(20\)
2. \(10\sqrt3\)
3. zero
4. \(10\)
1. \(10\) ms–1
2. zero
3. \(5\sqrt3\) ms–1
4. \(5\) ms–1
1. \(5\) m
2. \(10\) m
3. \(20\) m
4. \(25\) m
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. | \( \theta=\sin ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\) | 2. | \(\theta=\sin ^{-1}\left(\dfrac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) |
| 3. | \(\theta=\cos ^{-1}\left(\dfrac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) | 4. | \(\theta=\cos ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |
A projectile is fired from the surface of the earth with a velocity of \(5\) ms–1 and at an angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3\) ms–1 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 \(g=9.8\) ms–2)
1. \(3.5\) m/s2
2. \(5.9\) m/s2
3. \(16.3\) m/s2
4. \(110.8\) m/s2
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. | \(-2\hat i-3\hat j~\) |
1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)
2. \(\theta = \tan^{-1}(4)\)
3. \(\theta = \tan^{-1}(2)\)
4. \(\theta = 45^{\circ}\)
A missile is fired for a maximum range with an initial velocity of \(20\) m/s. If \(g=10\) m/s2, then the range of the missile will be:
| 1. | \(50\) m | 2. | \(60\) m |
| 3. | \(20\) m | 4. | \(40\) m |
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