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Q. No.A ball, thrown vertically upward, is observed to move upward with a speed \(v_1\) at time \(t_1\) and a speed \(v_2,\) downward, at time \(t_2.\)
The acceleration of the ball is (downward):
The acceleration of the ball is (downward):
| 1. | \(\dfrac{v_2-v_1}{t_2-t_1}\) | 2. | \(\dfrac{v_2+v_1}{t_2-t_1}\) |
| 3. | \(\dfrac{v_2-v_1}{t_2+t_1}\) | 4. | \(\dfrac{v_2+v_1}{t_2+t_1}\) |
Subtopic: Acceleration |
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%
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 particles move with constant speeds of \(3~\text{m/s}\) and \(5~\text{m/s}\) along the periphery of a square \(ABCD\) of side \(2~\text{m}\) (as shown). They start from \(A\) at the same time.
Their average accelerations, over the motion till they meet for the first time, are:
Their average accelerations, over the motion till they meet for the first time, are:
| 1. | \(3\sqrt2~\text{m/s}^2,5\sqrt2~\text{m/s}^2 \) | 2. | \(3~\text{m/s}^2,5~\text{m/s}^2 \) |
| 3. | \(3\sqrt2~\text{m/s}^2,10~\text{m/s}^2 \) | 4. | \(6~\text{m/s}^2,10~\text{m/s}^2 \) |
Subtopic: Acceleration |
Level 3: 35%-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
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 |
57%
Level 3: 35%-60%
Please attempt this question first.
Hints
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