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Q. No.Two cars \(A\) and \(B\) are moving in the same direction along a straight road with speeds \(100~\text{km/h}\) and \(80~\text{km/h},\) respectively. Car \(A\) is ahead of car \(B.\) Car \(B\) throws a stone in the direction of motion of the cars with speed \(v\) relative to car \(B.\) The stone strikes car \(A\) with a speed of \(5~\text {m/s}.\) relative to car \(A.\) The value of \(v,\) in km/h, is:
1. \(18\)
2. \(28\)
3. \(38\)
4. \(48\)
Subtopic: Â Relative Motion in One Dimension |
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The equation of motion of a particle is given by \(x =a\sin\left(50t+ \dfrac{\pi}{3}\right)~\text{cm}.\) The particle will come to rest at time \(t_1\) and it will have zero acceleration at time \(t_2\). The \(t_1\) and \(t_2\) respectively are:
1. \(\dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{75} ~\text{s} \)
2. \( \dfrac{\pi}{75} ~\text{s}, \dfrac{\pi}{300} ~\text{s}\)
3. \( \dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{25} ~\text{s}\)
4. \( \dfrac{\pi}{50} ~\text{s}, \dfrac{\pi}{100} ~\text{s}\)
1. \(\dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{75} ~\text{s} \)
2. \( \dfrac{\pi}{75} ~\text{s}, \dfrac{\pi}{300} ~\text{s}\)
3. \( \dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{25} ~\text{s}\)
4. \( \dfrac{\pi}{50} ~\text{s}, \dfrac{\pi}{100} ~\text{s}\)
Subtopic: Â Acceleration |
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Level 2: 60%+
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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: Â Uniformly Accelerated Motion |
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Level 1: 80%+
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The velocity (\(v\)) versus time (\(t\)) plot of a particle is shown in the figure, for a time interval of \(40~\text{s}\). The total distance travelled by the particle and the average velocity during this period are, respectively:
1. \(25~\text{m} \) and zero
2. \(50~\text{m}\) and zero
3. \(100~\text{m}\) and zero
4. \(100 ~\text{m}\) and \(2.5~\text{m/s}~\)
1. \(25~\text{m} \) and zero
2. \(50~\text{m}\) and zero
3. \(100~\text{m}\) and zero
4. \(100 ~\text{m}\) and \(2.5~\text{m/s}~\)
Subtopic: Â Graphs |
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Level 1: 80%+
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A new unit (\(a\)) length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of a units if light takes \(6\) min. \(40~\text{s}\) to cover this distance?
1. \(200~a\)
2. \(400~a\)
3. \(300~a\)
4. \(500~a\)
1. \(200~a\)
2. \(400~a\)
3. \(300~a\)
4. \(500~a\)
Subtopic: Â Distance & Displacement |
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Level 1: 80%+
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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: Â Uniformly Accelerated Motion |
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Level 2: 60%+
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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: Â Uniformly Accelerated Motion |
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Level 2: 60%+
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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: Â Uniformly Accelerated Motion |
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Level 1: 80%+
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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: Â Uniformly Accelerated Motion |
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Level 2: 60%+
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The velocity \( (v)\) - Distance \((x)\) graph is shown in figure. Which graph represents \((a)\) versus distance \((x)\) variation of this system?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Graphs |
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Level 3: 35%-60%
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