Q. No.| Assertion (A): | If two particles move with uniform accelerations in different directions, then their relative velocity changes in direction. |
| Reason (R): | Since the acceleration are in different directions, there is a relative acceleration and hence the relative velocity changes. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
Two guns, mounted along the forward and rear directions of a moving railroad car, are firing at the same angle (relative to the car). The shells rise to a height of 500 m. The forward range of the shells is more than the backward gun's range by 200m. The speed of the railroad car is (take g = 10 m/s2)
Hint: The range is increased/decreased due to the movement of the car by Vcar·Tshell.
1. 5 m/s
2. 10 m/s
3. 20 m/s
4. 40 m/s
It can be concluded that:
| 1. | \(v_1>v_2\) |
| 2. | \(v_1<v_2\) |
| 3. | \(v_1=v_2\) |
| 4. | Any of the above can be true depending on the angle of projection |
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
A man drifting on a raft on a river observes a boat moving in the same direction at a relative speed which is \(3\) times the speed of the river's flow of \(3\) km/h. The boat overtakes him at a certain moment and reaches a point downstream after a time \(T_B\) while he reaches the same point after \(T_A=3 \) hr. Then, \(T_B= \)
| 1. | \(1\) hr | 2. | \(\dfrac12\)hr |
| 3. | \(\dfrac23\) hr | 4. | \(\dfrac34\) hr |
| 1. | \(1\) | 2. | \(\dfrac{2}{\pi} \) |
| 3. | \(\dfrac{4}{\pi^2} \) | 4. | \(\sqrt{\dfrac{2}{\pi}} \) |
| 1. | greater than \(1000\) m |
| 2. | less than \(1000\) m |
| 3. | equal to \(1000\) m |
| 4. | can be any of the above depending on the height of the cliff |
1. zero
2. \((\pi-1)~\text{m/s}\)
3. \(\sqrt{\pi^2+1}~\text{m/s}\)
4. \(\sqrt{\pi^2-1}~\text{m/s}\)
\({A}\) throws a ball towards \({B},\) who then catches it across the field. \({B}\) throws the ball back towards \({A},\) who then catches it. The angle of the throw is \(30^\circ\) for \({A},\) while it is \(60^\circ\) for \({B}'\text{s}\) throw. The ratio of their speeds of throw, \({v_A}: {v_B}\) is:
1. \(3\)
2. \(\dfrac13\)
3. \(\sqrt3\)
4. \(1\)
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