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Q. No.A particle is projected vertically upwards with a speed \(u\) and moves under the force of gravity. The distance travelled by the particle during its entire motion (until it returns) is \(d_1.\) If the force of gravity were to be switched off, and the particle travelled for the same length of time, then the distance travelled is \(d_2.\) Then,
1. \(d_2 = d_1\)
2. \(d_2 = 2d_1\)
3. \(d_2 = 3d_1\)
4. \(d_2 = 4 d_1\)
Subtopic: Uniformly Accelerated Motion |
54%
Level 3: 35%-60%
Hints
The velocity-time graph of a particle, moving along a straight time, is shown in the figure. The curve, when plotted, takes the form of a 'circle'. The magnitude of the average acceleration of the particle is:
| 1. | \(1\) m/s2 |
| 2. | \(2\) m/s2 |
| 3. | less than \(1\) m/s2 |
| 4. | greater than \(2\) m/s2 |
Subtopic: Acceleration |
61%
Level 2: 60%+
Hints
Two cars \(A\) and \(B\) start moving along the same straight road, from the same point, simultaneously. The first car \((A)\) accelerates uniformly to a maximum speed of \(v_0\) and then decelerates uniformly to a stop. The second car \((B)\) accelerates uniformly to the same maximum speed \(v_0\) and then decelerates uniformly to a stop. The acceleration of \(A\) is twice that of \(B,\) and they both spend the same total time during the motion. Then,
Choose the correct option from the given ones:
| (A) | distance travelled by \(A\) = distance travelled by \(B\) |
| (B) | acceleration time of \(A\) = \(\dfrac12\) acceleration time of \(B\) |
| (C) | relative velocity of \(A\) with respect to \(B\) is always positive |
| (D) | deceleration time of \(A\) = \(2×\) deceleration time of \(B\) |
Choose the correct option from the given ones:
| 1. | (A) is True. |
| 2. | (A), (B) are True. |
| 3. | (A), (B), (C) are True. |
| 4. | (B), (C), (D) are True. |
Subtopic: Acceleration |
Level 3: 35%-60%
Hints
A ball \((A)\) is projected vertically upward; a second ball \((B)\) is projected horizontally with the same initial speed as the first. The relative velocity of ball \(A\) with respect to \(B\):
| 1. | is constant in magnitude only |
| 2. | is constant in direction |
| 3. | is constant in magnitude and direction |
| 4. | varies, both in magnitude and direction |
Subtopic: Relative Motion in One Dimension |
Level 3: 35%-60%
Hints
A particle moves along a straight line such that its velocity is proportional to the square root of its displacement. Its acceleration is:
| 1. | zero |
| 2. | constant |
| 3. | proportional to time |
| 4. | proportional to displacement |
Subtopic: Acceleration |
69%
Level 2: 60%+
Hints
A small particle slides up and down along a smooth path \(ABC~(\angle B=90^{\circ}), \) under the action of gravity, coming to a stop briefly at the highest points \((A,C)\) of the path \(ABC.\) The path is rounded at \(B \) to facilitate the back and forth motion. The time taken for the particle to go from \(A\) to \(C\) is
| 1. | \(\sqrt{\dfrac{2h}{g}}(\sin\theta+\cos\theta) \) |
| 2. | \(\sqrt{\dfrac{2h}{g}}(\sin^2\theta+\cos^2\theta) \) |
| 3. | \(\sqrt{\dfrac{2h}{g}}\left(\dfrac1{\sin\theta}+\dfrac1{\cos\theta}\right) \) |
| 4. | \(\sqrt{\dfrac{2h}{g}}\left(\dfrac1{\sin^2\theta\cdot \cos^2\theta}\right) \) |
Subtopic: Acceleration |
53%
Level 3: 35%-60%
Hints
Two stones \(A\) and \(B\) are projected simultaneously with the same speed: one \((A)\) vertically up and the other \((B)\) horizontally from the same point. Stone \(A\) rises up to a maximum height \(H\) and falls down. The separation between \(A\) and \(B,\) when \(A\) reaches its maximum height:
| 1. | is less than \(H\) |
| 2. | is greater than \(H\) |
| 3. | is equal to \(H\) |
| 4. | cannot be related with \(H\) |
Subtopic: Uniformly Accelerated Motion |
62%
Level 2: 60%+
Hints
A balloon ascends upward with a constant upward velocity \(5\) m/s. At the same time, it is being pushed to the right by the wind with a speed that is proportional to its height \((y)\): \(v_\text{right}=2y \)
where the units are in SI. The acceleration of the balloon is:
1. zero
2. \(10~\text{ms}^{-2}\) to right
3. \(5~\text{ms}^{-2}\) to right
4. \(10~\text{ms}^{-2}\) upward
where the units are in SI. The acceleration of the balloon is:
1. zero
2. \(10~\text{ms}^{-2}\) to right
3. \(5~\text{ms}^{-2}\) to right
4. \(10~\text{ms}^{-2}\) upward
Subtopic: Acceleration |
Level 3: 35%-60%
Hints
Two cars \(A\) and \(B,\) each \(5~\text{m}\) long, are travelling along parallel lanes with speeds of \(36~\text{km/hr}\) and \(72~\text{km/hr}.\) The car \(B\) is just behind the car \(A,\) but is beginning to overtake. What will be the distance covered by the car \(B\) by the time it is just ahead of the car \(A?\)
1. \(10~\text{m}\)
2. \(15~\text{m}\)
3. \(20~\text{m}\)
4. \(25~\text{m}\)
1. \(10~\text{m}\)
2. \(15~\text{m}\)
3. \(20~\text{m}\)
4. \(25~\text{m}\)
Subtopic: Relative Motion in One Dimension |
Level 3: 35%-60%
Hints
The velocity-time graph of a particle moving along a straight line is shown in the adjacent figure. The average velocity is:
| 1. | \(1~\text{ms}^{-1}\) | 2. | \(2~\text{ms}^{-1}\) m/s |
| 3. | less than \(1~\text{ms}^{-1}\) | 4. | greater than \(2~\text{ms}^{-1}\) |
Subtopic: Graphs |
Level 3: 35%-60%
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