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Q. No.A bullet is shot vertically downwards with an initial velocity of \(100\) m/s from a certain height. Within \(10\) s, the bullet reaches the ground and instantaneously comes to rest due to a perfectly inelastic collision. The velocity-time curve for total time \(t=20 \) s is: (take \(g=10\) m/s2 )
1.
2.
3.
4.
Subtopic: Graphs |
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Level 3: 35%-60%
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A ball is thrown vertically upwards with a velocity of \(19.6~\text{ms}^{-1}\) from the top of a tower. The ball strikes the ground after \(6~\text s.\) The height from the ground up to which the ball can rise will be \(\left ( \dfrac{k}{5} \right )~\text {m}.\)The value of \(k\) is:
(use \(g=9.8~\text{ms}^{-2})\)
1. \(392 \)
2. \(360\)
3. \(315\)
4. \(420\)
(use \(g=9.8~\text{ms}^{-2})\)
1. \(392 \)
2. \(360\)
3. \(315\)
4. \(420\)
Subtopic: Uniformly Accelerated Motion |
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Level 2: 60%+
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A particle moves along a straight line with its velocity \((v)\) varying as the square root of its displacement \((x)\text:\) \(v\propto\sqrt x\)
Then its acceleration varies as:
1. \(\dfrac{1}{\sqrt x}\)
2. \(x^{3/2}\)
3. \(x^{-3/2}\)
4. \(x^0\)
Then its acceleration varies as:
1. \(\dfrac{1}{\sqrt x}\)
2. \(x^{3/2}\)
3. \(x^{-3/2}\)
4. \(x^0\)
Subtopic: Acceleration |
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Level 3: 35%-60%
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An athlete runs along a straight track. She begins from rest and accelerates uniformly for \(2~\text{s},\) reaching a speed of \(9~\text{m/s}.\) She then runs at this constant speed for a certain duration before decelerating uniformly to rest. The total time from start to finish is \(12~\text s.\) If her acceleration during the first phase is exactly twice the magnitude of her deceleration during the last phase, what is the total distance she covers during the entire motion?
1. \(81~\text{m}\)
2. \(108~\text{m}\)
3. \(90~\text{m}\)
4. \(72~\text{m}\)
1. \(81~\text{m}\)
2. \(108~\text{m}\)
3. \(90~\text{m}\)
4. \(72~\text{m}\)
Subtopic: Distance & Displacement |
59%
Level 3: 35%-60%
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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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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%
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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%
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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 |
54%
Level 3: 35%-60%
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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%
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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%
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