Q. No.The ratio of the distances travelled by a freely falling body in the \(1\)st, \(2\)nd, \(3\)rd and \(4\)th second is:
1.
\(1:1:1:1\)
2.
\(1:2:3:4\)
3.
\(1:4:9:16\)
4.
\(1:3:5:7\)
The figure given below shows the displacement and time, \((x\text -t)\) graph of a particle moving along a straight line:
The correct statement, about the motion of the particle, is:
| 1. | the particle moves at a constant velocity up to a time \(t_0\) and then stops. |
| 2. | the particle is accelerated throughout its motion. |
| 3. | the particle is accelerated continuously for time \(t_0\) then moves with constant velocity. |
| 4. | the particle is at rest. |
| 1. | \(1: \sqrt{3}\) | 2. | \(\sqrt{3}: 1\) |
| 3. | \(1:1\) | 4. | \(1:2\) |
1. \(4~\text m\)
2. zero
3. \(6~\text m\)
4. \(2~\text m\)
| 1. | \(\dfrac{3v}{4}\) | 2. | \(\dfrac{v}{3}\) |
| 3. | \(\dfrac{2v}{3}\) | 4. | \(\dfrac{4v}{3}\) |
(Take \(g=10~ \text {ms}^{-2}\) )
| 1. | \(68\) m | 2. | \(56\) m |
| 3. | \(60\) m | 4. | \(64\) m |
A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is:
| 1. | \(\dfrac{2n+1}{2n-1}\) | 2. | \(\dfrac{2n}{2n-1}\) |
| 3. | \(\dfrac{2n-1}{2n}\) | 4. | \(\dfrac{2n-1}{2n+1}\) |
The acceleration \((a)\)-time \((t)\) graph that best suits this motion is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| 1. | \(5~\text{m}\) | 2. | \(25~\text{m}\) |
| 3. | \(45~\text{m}\) | 4. | \(58~\text{m}\) |
A body is falling freely in a resistive medium. The motion of the body is described by \(\dfrac{dv}{dt}=(4-2v), \) where \(v\) is the velocity of the body at any instant (in \(\text{ms}^{–1}\)). The terminal velocity in this case refers to the velocity the body approaches as time \(t \to \infty.\) The initial acceleration and terminal velocity of the body, respectively, are:
| 1. | \(4~\text{m/s}^2,\) \(2~\text{m/s}\) | 2. | \(2~\text{m/s}^2,\) \(4~\text{m/s}\) |
| 3. | \(6~\text{m/s}^2,\) \(2~\text{m/s}\) | 4. | \(2~\text{m/s}^2,\) \(6~\text{m/s}\) |
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