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:  Relative Motion |
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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:  Relative Motion |
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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. \(\sqrt{\pi^2-1}~\text{m/s}\)
Subtopic:  Relative Motion |
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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. \(v_r=4~\mathrm{cosec }\theta_r~\text{m/s}\)
Subtopic:  Relative Motion |
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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:  Relative Motion |
 51%
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