Q. No.A particle moves along a straight line so that its velocity \((v)\) is directed towards a fixed point on its path and is proportional to its distance \((x)\) from that point. Its acceleration is proportional to:
| 1. | \(x\) | 2. | \(\dfrac1x\) |
| 3. | \(\sqrt x\) | 4. | \(\dfrac{1}{\sqrt x}\) |
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A boy throws a ball straight up the side of a building and receives it after \(4\) s. On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after \(3\) s. The ledge is at a distance \(d\) below the highest point, where \(d=?\) (take acceleration due to gravity, \(g=10\) m/s2)
1. \(5\) m
2. \(2.5\) m
3. \(1.25\) m
4. \(10\) m
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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. \(10~\text{m/s}\)
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A particle moves around a circle with a unique uniform speed in each revolution. After the first revolution and during the \(2\)nd revolution: its speed doubles; and during the \(3\)rd revolution, its speed becomes \(3\) times the initial speed and so on. The time for the \(1\)st revolution is \(12\) sec. The average time per revolution, for the first four revolutions, is:
1. \(4.8\) s
2. \(9.6\) s
3. \(6.25\) s
4. \(6\) s
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| 1. | The acceleration is constant and non-zero. |
| 2. | The velocity changes suddenly during the motion. |
| 3. | The velocity is positive throughout. |
| 4. | All of the above are true. |
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1. \(d_2 = d_1\)
2. \(d_2 = 2d_1\)
3. \(d_2 = 3d_1\)
4. \(d_2 = 4 d_1\)
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| 1. | \(1\) m/s2 |
| 2. | \(2\) m/s2 |
| 3. | less than \(1\) m/s2 |
| 4. | greater than \(2\) m/s2 |
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| (A) | distance travelled by \(A\) = distance travelled by \(B\) |
| (B) | acceleration time of \(A\) = \(\dfrac12\) acceleration time of \(B\) |
| (C) | relative velocity of \(A\) with respect to \(B\) is always positive |
| (D) | deceleration time of \(A\) = \(2×\) deceleration time of \(B\) |
Choose the correct option from the given ones:
| 1. | (A) is True. |
| 2. | (A), (B) are True. |
| 3. | (A), (B), (C) are True. |
| 4. | (B), (C), (D) are True. |
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| 1. | is constant in magnitude only. |
| 2. | is constant in direction. |
| 3. | is constant in magnitude and direction. |
| 4. | varies, both, in magnitude and direction. |
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| 1. | zero |
| 2. | constant |
| 3. | proportional to time |
| 4. | proportional to displacement |
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