Q. No.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 |
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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 |
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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 |
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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 |
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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 |
 50%
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A man, swimming with a speed \(u_1,\) can cross a river fastest in a time, \(T\). His friend, who swims with a speed \(u_2,\) reaches the opposite bank in the same time when he swims at an angle of \(30^{\circ}\) with the bank. Then:
| 1. | \(u_1=\dfrac{\sqrt3}{2}u_2\) | 2. | \(u_1=\dfrac{1}{2}u_2\) |
| 3. | \(u_1=\dfrac{1}{\sqrt2}u_2\) | 4. | \(u_1=\dfrac{1}{\sqrt3}u_2\) |
Subtopic: Â Relative Motion |
 58%
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A boat is rowed across a \(400~\text m\) wide river so that it can reach the opposite bank in a minimum of \(10\) minutes. No matter which direction the boat is rowed in, it cannot reach a point exactly opposite on the other bank, unless it is rowed at a slightly higher speed. The speed of flow of the river is:
| 1. | \(2.4~\text{km/h}\) | 2. | \(4.8~\text{km/h}\) |
| 3. | \(2.4\sqrt2~\text{km/h}\) | 4. | \(\dfrac{2.4}{\sqrt2}~\text{km/h}\) |
Subtopic: Â Relative Motion |
 59%
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A boat, when rowed perpendicular to the flow of a \(500\) m wide river, reaches its opposite bank in \(10\) min. If the boat is rowed downstream at an angle of \(30^\circ\) with the flow, it will cross in:
| 1. | \(10\) min | 2. | \(5\sqrt3\) min |
| 3. | \(20\) min | 4. | \(\dfrac{10}{\sqrt3}\) min |
Subtopic: Â Relative Motion |
 60%
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Raindrops fall from the sky making an angle of \(30^\circ\) with the vertical. If a man runs at \(2\) m/s, he finds that the drops fall vertically. If he were to run in the opposite direction with the same speed\(,\) the raindrops will fall with a vertical speed of:
| 1. | \(2\) m/s | 2. | \(4\) m/s |
| 3. | \(2\sqrt3 \) m/s | 4. | \(4\sqrt3 \) m/s |
Subtopic: Â Relative Motion |
 62%
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Given below are two statements:
| Assertion (A): | If the velocities of two particles are perpendicular to each other, then their separation must be increasing with time. |
| Reason (R): | The relative velocity between the two particles is higher in magnitude than either of them. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Relative Motion |
 52%
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