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Q. No.A ball is thrown at an angle \(\theta_0\) above the horizontal, and follows the parabolic path taken by a projectile. Let its speed be \(v\) when its trajectory makes an angle \(\theta\) with the horizontal. Assuming \(A\) to be a constant,
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
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%
Hints
The average velocity of a projectile from the point of projection to impact is \(v_1\) while the average velocity from projection to maximum height\((H)\) is \(v_2\).
It can be concluded that:
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 |
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
A projectile is launched at an angle \(\theta~(<90^{\circ})\) above the horizontal. Its velocity is measured along the direction of projection and is plotted against time and the magnitudes of the slopes are indicated in the figure below. Which of the following is the correct graph?
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
A particle \((1),\) dropped from rest from the topmost point \((A)\) of a vertical circle, reaches the bottom \((B)\) in the same time as when a second particle \((2)\) moving with constant speed moves along the circumference from \(A\) to \(B.\) The ratio of the accelerations of the particles \((a_1/a_2)\) equals:
| 1. | \(1\) | 2. | \(\dfrac{2}{\pi} \) |
| 3. | \(\dfrac{4}{\pi^2} \) | 4. | \(\sqrt{\dfrac{2}{\pi}} \) |
Subtopic: Â Circular Motion |
Level 3: 35%-60%
Hints
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%
Hints
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%
Hints
Match the shapes of the paths in Column I with the possible accelerations mentioned under Column II.
| 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. | \(\mathrm{A\text-I;B\text-II,III;C\text-II;D\text-IV}\) |
Subtopic: Â Circular Motion |
 51%
Level 3: 35%-60%
Hints
A projectile is fired from the top of a cliff, the maximum range of the projectile being \(1000\) m on level ground. The maximum range of the projectile, measured from the base of the cliff is:
| 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 |
Subtopic: Â Projectile Motion |
Level 3: 35%-60%
Hints
Two particles \(A,B\) move along the periphery of a circle of radius \(R,\) with the same uniform speed \(u.\) Particle \(A\) follows \(B,\) a quarter of the circumference behind it. The acceleration of \(A\) relative to \(B\) is:
| 1. | zero | 2. | \(\dfrac{2u^2}{R}\) |
| 3. | \(\dfrac{u^2}{\sqrt2R}\) | 4. | \(\dfrac{\sqrt2u^2}{R}\) |
Subtopic: Â Circular Motion |
 50%
Level 3: 35%-60%
Hints
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