Q. No.1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
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| 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). |
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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 |
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1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
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| 1. | \(1\) | 2. | \(\dfrac{2}{\pi} \) |
| 3. | \(\dfrac{4}{\pi^2} \) | 4. | \(\sqrt{\dfrac{2}{\pi}} \) |
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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 |
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1. zero
2. \((\pi-1)~\text{m/s}\)
3. \(\sqrt{\pi^2+1}~\text{m/s}\)
4. \(\sqrt{\pi^2-1}~\text{m/s}\)
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| Column I | Column II | ||
| \(\mathrm{(A)}\) | Straight line | \(\mathrm{(I)}\) | \(\vec a=\text{constant}\) |
| \(\mathrm{(B)}\) | Circle | \(\mathrm{(II)}\) | \(a_t~\text{(tangential)}=0\\ a_c~\text{(centripetal)}\neq0\) |
| \(\mathrm{(C)}\) | Parabola | \(\mathrm{(III)}\) | \(a_t~\text{(tangential)}\neq0\\ a_c~\text{(centripetal)}=0\) |
| \(\mathrm{(D)}\) | Ellipse | \(\mathrm{(IV)}\) | \(a_t~\text{(tangential)}\neq0\\ a_c~\text{(centripetal)}\neq0\) |
| 1. | \(\mathrm{A\text-I,III;B\text-II,IV;C\text-I,II,IV;D\text-II,IV}\) |
| 2. | \(\mathrm{A\text-I;B\text-II,IV;C\text-I,IV;D\text-I,IV}\) |
| 3. | \(\mathrm{A\text-II,IV;B\text-I,III;C\text-II,IV;D\text-III,IV}\) |
| 4. | \(\mathrm{A\text-I;B\text-II,III;C\text-II;D\text-IV}\) |
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| 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 |
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| 1. | zero | 2. | \(\dfrac{2u^2}{R}\) |
| 3. | \(\dfrac{u^2}{\sqrt2R}\) | 4. | \(\dfrac{\sqrt2u^2}{R}\) |
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