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Q. No.A ball is dropped vertically from height \(h\) and bounces elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time?
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4. |  |
A particle projected vertically under gravity passes a certain level on the way up at a time \(T_1\) and on the way down at a time \(T_2\) – after it was projected. The speed of projection is:
1. \(\dfrac{1}{2} g\left(T_{1}+T_{2}\right)\)
2. \(\dfrac{1}{2} g\left(T_{1}-T_{2}\right)\)
3. \(g \sqrt{T_{1} T_{2}}\)
4. \(\dfrac{1}{2} g \dfrac{T_{1} T_{2}}{T_{1}+T_{2}}\)
A boy throws a ball straight up the side of a building and receives it after \(4~\text s.\) On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after \(3~\text s.\) The ledge is at a distance \(d\) below the highest point, where \(d=? \) (take acceleration due to gravity, \(g=10~\text{ms}^{-2})\)
| 1. | \(5~\text m\) | 2. | \(2.5~\text m\) |
| 3. | \(1.25~\text m\) | 4. | \(10~\text m\) |
A man driving a scooter at \(15~\text{m/s}\) brakes at the rate of \(2~\text{m/s}^2\). His speed, after \(10~\text{s}\) after the application of brakes will be:
1. \(5~\text{m/s}\)
2. \(-5~\text{m/s}\)
3. \(0~\text{m/s}\)
4. \(10~\text{m/s}\)
(use \(g=9.8~\text{ms}^{-2})\)
1. \(392 \)
2. \(360\)
3. \(315\)
4. \(420\)
| Particles\(\rightarrow\) | \(A\) | \(B\) |
| initial velocity | \(-\vec u\) | \(\vec u\) |
| acceleration | \(\vec a\) | zero |
| 1. | \(2\vec ut+{\large\frac12}\vec at^2\) | 2. | \(2\vec ut-{\large\frac12}\vec at^2\) |
| 3. | \({\large\frac12}\vec at^2\) | 4. | \(-{\large\frac12}\vec at^2\) |
1. \(d_2 = d_1\)
2. \(d_2 = 2d_1\)
3. \(d_2 = 3d_1\)
4. \(d_2 = 4 d_1\)
| 1. | \(\sqrt{\dfrac{2h}{g}}(\sin\theta+\cos\theta) \) |
| 2. | \(\sqrt{\dfrac{2h}{g}}(\sin^2\theta+\cos^2\theta) \) |
| 3. | \(\sqrt{\dfrac{2h}{g}}\left(\dfrac1{\sin\theta}+\dfrac1{\cos\theta}\right) \) |
| 4. | \(\sqrt{\dfrac{2h}{g}}\left(\dfrac1{\sin^2\theta\cdot \cos^2\theta}\right) \) |
A man \((A)\) has to throw a ball vertically up to a partner \((B)\) who is standing up, above his level by \(15~\text{m}.\) The \((B)\) partner can catch the ball only when it comes downwards with a maximum speed of \(10~\text{m/s}\)
(take acceleration due to gravity as \(10~\text{m/s}^{2}\))
The minimum and maximum speeds of the throw are: (nearly)
1. \(10~\text{m/s}~\text{and}~20~\text{m/s}\)
2. \(10~\text{m/s}~\text{and}~30~\text{m/s}\)
3. \(20~\text{m/s}~\text{and}~20\sqrt{3}~\text{m/s}\)
4. \(10\sqrt{3}~\text{m/s}~\text{and}~20~\text{m/s}\)
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Q. No.
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