Q. No.From \(18~\text m\) height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is: (in m)
\((\text{Take} ~g = 10~\text{m/s}^ 2)\) and neglect the air resistance)
1. \(12\)
2. \(13\)
3. \(15\)
4. \(18\)
\((\text{Take} ~g = 10~\text{m/s}^ 2)\) and neglect the air resistance)
1. \(12\)
2. \(13\)
3. \(15\)
4. \(18\)
Subtopic: Uniformly Accelerated Motion |
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A gas balloon is going up with a constant velocity of \(10~\text{m/s}\) \(g=10~\text{m/s}^2\)
1. \(85\)
2. \(150\)
3. \(129\)
4. \(125\)
1. \(85\)
2. \(150\)
3. \(129\)
4. \(125\)
Subtopic: Uniformly Accelerated Motion |
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Two masses of \(3.4~\text{kg}\) and \(2.5~\text{kg}\) are accelerated from an initial speed of \(5~\text{m/s}\) and \(12~\text{m/s}\), respectively. The distances traversed by the masses in the \(5^{\text{th}}\) second are \(104~\text{m}\) and \(129~\text{m}\), respectively. The ratio of their momentum after \(10~\text{s}\) is \(\dfrac{x}{8}\). The value of \(x\) is:
1. \(8\)
2. \(9\)
3. \(11\)
4. \(14\)
1. \(8\)
2. \(9\)
3. \(11\)
4. \(14\)
Subtopic: Uniformly Accelerated Motion |
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A block is sliding down on an inclined plane of slope \(\theta\) and at an instant \(t=0\) this block is given an upward momentum so that it starts moving up on the inclined surface with velocity \(u\). The distance \((S)\) travelled by the block before its velocity become zero, is:
(\(g=\) gravitational acceleration)
1. \(\dfrac{{u}^2}{4 {g} \sin \theta}\)
2. \(\dfrac{2 {u}^2}{{g} \cos \theta}\)
3. \(\dfrac{{u}^2}{\sqrt{2}{g} \cos \theta}\)
4. \(\dfrac{{u}^2}{2 {g} \sin \theta}\)
(\(g=\) gravitational acceleration)
1. \(\dfrac{{u}^2}{4 {g} \sin \theta}\)
2. \(\dfrac{2 {u}^2}{{g} \cos \theta}\)
3. \(\dfrac{{u}^2}{\sqrt{2}{g} \cos \theta}\)
4. \(\dfrac{{u}^2}{2 {g} \sin \theta}\)
Subtopic: Uniformly Accelerated Motion |
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A paratrooper jumps from an aeroplane and opens a parachute after \(2~\text{s}\) of free fall and starts deaccelerating with \(3~\text{m/s}^2\). At \(10\) m height from ground, while descending with the help of parachute, the speed of paratrooper is \(5\) m/s. The initial height of the aeroplane is: (in m)
\(\left(g=10~ \text{m/s}^2\right)\)
1. \(62.5\)
2. \(92.5\)
3. \(20\)
4. \(82.5\)
\(\left(g=10~ \text{m/s}^2\right)\)
1. \(62.5\)
2. \(92.5\)
3. \(20\)
4. \(82.5\)
Subtopic: Uniformly Accelerated Motion |
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Water drops fall from a tap on the floor, \(5~\text{m}\) below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is: (in m) \(\left(g=10~\text{m/s}^2\right)\)
1. \(2.5\)
2. \(4.0\)
3. \(4.2\)
4. \(3.8\)
1. \(2.5\)
2. \(4.0\)
3. \(4.2\)
4. \(3.8\)
Subtopic: Uniformly Accelerated Motion |
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The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first \(30.5\) second is:
1. \(3~\text{km}\)
2. \(6~\text{km}\)
3. \(9~\text{km}\)
4. \(12~\text{km}\)
1. \(3~\text{km}\)
2. \(6~\text{km}\)
3. \(9~\text{km}\)
4. \(12~\text{km}\)
Subtopic: Uniformly Accelerated Motion |
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A bus moving along a straight highway with speed of \(72~\text{km/h}\) is brought to halt within \(4~\text s\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is:
1. \(20~\text m\)
2. \(10~\text m\)
3. \(40~\text m\)
4. \(15~\text m\)
1. \(20~\text m\)
2. \(10~\text m\)
3. \(40~\text m\)
4. \(15~\text m\)
Subtopic: Uniformly Accelerated Motion |
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A body projected vertically upwards with a certain speed from the top of tower reaches the ground in \(t_1\). If it is projected vertically downwards from the same point with the same speed, it reaches the ground in \(t_2\). Time required to reach the ground, if it is dropped from the top of the tower is:
1. \(\sqrt{t_1+t_2}\)
2. \(\sqrt{t_1-t_2}\)
3. \(\sqrt{{t}_{{2}} {t}_{{1}}}\)
4. \(\sqrt{\dfrac{t_1}{t_2}} \)
1. \(\sqrt{t_1+t_2}\)
2. \(\sqrt{t_1-t_2}\)
3. \(\sqrt{{t}_{{2}} {t}_{{1}}}\)
4. \(\sqrt{\dfrac{t_1}{t_2}} \)
Subtopic: Uniformly Accelerated Motion |
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An object is dropped from rest at point \({P}.\) It crosses two points \({A}\) and \(B\) in a time interval of \(2~\text{s},\) where the distance \(AB=80~\text{m}.\) If \(g=10~\text{m/s}^2,\) then what is the distance \({AP} \) in metres?
| 1. | \(70\) | 2. | \(45\) |
| 3. | \(60\) | 4. | \(55\) |
Subtopic: Uniformly Accelerated Motion |
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