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Given below are two statements:
| 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). |
Subtopic: Â Relative Motion |
Level 4: Below 35%
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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 |
Subtopic: Â Relative Motion |
Level 3: 35%-60%
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A particle moves around a circle with a speed of \(\pi~\text{m/s},\) while another moves back-and-forth along a diameter with a speed of \(1~\text{m/s}.\) The minimum possible relative velocity between them is (in magnitude):
1. zero
2. \((\pi-1)~\text{m/s}\)
3. \(\sqrt{\pi^2+1}~\text{m/s}\)
4. \(\sqrt{\pi^2-1}~\text{m/s}\)
1. zero
2. \((\pi-1)~\text{m/s}\)
3. \(\sqrt{\pi^2+1}~\text{m/s}\)
4. \(\sqrt{\pi^2-1}~\text{m/s}\)
Subtopic: Â Relative Motion |
Level 3: 35%-60%
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A man walks in the rain, where the raindrops are falling vertically down at a constant speed of \(4~\text{m/s}\) relative to ground. Let the relative velocity of a droplet with respect to man be \(v_r\) and let it make an angle \(\theta_r\) with the vertical. Then:
1. \(v_r=4\cos\theta_r~\text{m/s}\)
2. \(v_r=4\sin\theta_r~\text{m/s}\)
3. \(v_r=4\sec\theta_r~\text{m/s}\)
4. \(v_r=4~\mathrm{cosec }\theta_r~\text{m/s}\)
1. \(v_r=4\cos\theta_r~\text{m/s}\)
2. \(v_r=4\sin\theta_r~\text{m/s}\)
3. \(v_r=4\sec\theta_r~\text{m/s}\)
4. \(v_r=4~\mathrm{cosec }\theta_r~\text{m/s}\)
Subtopic: Â Relative Motion |
 51%
Level 3: 35%-60%
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Two particles \(A\), \(B\) are projected simultaneously from the base of a triangle \(ABC\). Particle \(A\) is projected from vertex \(A\) along \(AC,\) and particle \(B\) is projected from vertex \(B\) along \(BC\). Their respective velocities are \(v_A\) & \(v_B\) and they move with uniform velocities. For the particles to collide:
| 1. | \(v_A~\text{cos}A=v_B~\text{cos}B\) |
| 2. | \(v_A~\text{sin}A=v_B~\text{sin}B\) |
| 3. | \(\dfrac{v_A}{\text{sin}A}=\dfrac{v_B}{\text{sin}B}\) |
| 4. | \(v_A~\text{tan}A=v_B~\text{tan}B\) |
Subtopic: Â Relative Motion |
 54%
Level 3: 35%-60%
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