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Q. No.A particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that its centripetal acceleration (\(a\)) is varying with time \(t\) as \(a=k^2rt^2\) where \(k\) is a constant. The power delivered to the particle by the force acting on it is given as:
1. zero
2. \( {m k^2} {r^2} t^2 \)
3. \({mk}^2 {r}^2 {t} \)
4. \({mk}^2 {rt}\)
Subtopic: Power |
Level 3: 35%-60%
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A man of \(60\) kg is running on the road and suddenly jumps into a stationary trolly car of mass \(120\) kg. Then, the trolly car starts moving with a velocity of \(2\) ms–1. The velocity of the running man just before jumping into trolly car was:
1. \(4\) ms–1
2. \(2\) ms–1
3. \(3\) ms–1
4. \(6\) ms–1
1. \(4\) ms–1
2. \(2\) ms–1
3. \(3\) ms–1
4. \(6\) ms–1
Subtopic: Collisions |
78%
Level 2: 60%+
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A block of mass \(2~\text{kg},\) moving with a speed of \(4~\text{m/s}\) on a horizontal surface enters a rough region extending from \(x =0.5~\text{m}\) to \(x =1.5~\text{m}.\) In this region, the retarding force is given by \(F = -kx\) with \(k=12~\text{N/m}.\) What will be the speed of the block as it just emerges from the rough surface?
| 1. | \(0\) | 2. | \(1.5~\text{m/s}\) |
| 3. | \(2.0~\text{m/s}\) | 4. | \(2.5~\text{m/s}\) |
Subtopic: Work Energy Theorem |
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Level 2: 60%+
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Water is falling from a \(40\) m high dam at the rate of \(9 \times 10^4\) kg per hour. Fifty percent of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of \(100\) W bulbs, that can be lit, is:
(Take \(g=10\) ms–2)
1. \(25\)
2. \(50\)
3. \(100\)
4. \(18\)
(Take \(g=10\) ms–2)
1. \(25\)
2. \(50\)
3. \(100\)
4. \(18\)
Subtopic: Gravitational Potential Energy |
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Level 2: 60%+
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A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{\mathrm{x}\left(\mathrm{u}^2-\mathrm{gL}\right)}\). The value of x is:
1. 3
2. 2
3. 1
4. 5
1. 3
2. 2
3. 1
4. 5
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed \(v \over 3\) and the bob just completes the vertical circle. The value of v is: (if g = 10 m/s2 )
1. 10 ms–1
2. 20 ms–1
3. 30 ms–1
4. 40 ms–1
1. 10 ms–1
2. 20 ms–1
3. 30 ms–1
4. 40 ms–1
Subtopic: Collisions |
74%
Level 2: 60%+
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A moving particle collides head-on elastically with a stationary particle whose mass is five times that of the moving particle.
What percentage of the kinetic energy of the moving particle is transferred to the stationary particle during the collision?
1. \(50.0\)%
2. \(66.6\)%
3. \(55.5\)%
4. \(33.3\)%
What percentage of the kinetic energy of the moving particle is transferred to the stationary particle during the collision?
1. \(50.0\)%
2. \(66.6\)%
3. \(55.5\)%
4. \(33.3\)%
Subtopic: Collisions |
65%
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Arrange the four graphs in descending order of total work done; where \(W_1, W_2, W_3 ~\text{and}~W_4\) are the work done corresponding to figures \(a,b,c~\text{and}~d\) respectively.
| 1. | \( W_3>W_2>W_1>W_4 \) |
| 2. | \( W_3>W_2>W_4>W_1 \) |
| 3. | \({W}_2>{W}_3>{W}_4>{W}_1 \) |
| 4. | \(W_2>W_3>W_1>W_4\) |
Subtopic: Work Done by Variable Force |
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An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?
1. momentum
2. potential energy
3. acceleration
4. force
1. momentum
2. potential energy
3. acceleration
4. force
Subtopic: Conservation of Mechanical Energy |
83%
Level 1: 80%+
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Potential energy as a function of \({r}\) is given by; \({U}=\dfrac{{A}}{{r}^{10}}-\dfrac{{B}}{{r}^5},\) where \({r}\) is the interatomic distance, and \({A}\) and \({B}\) are positive constants. The equilibrium distance between the two atoms will be:
| 1. | \(\left ( \dfrac{{A}}{{B}}\right )^{1/5}\) | 2. | \(\left ( \dfrac{{B}}{{A}}\right )^{1/5}\) |
| 3. | \(\left ( \dfrac{{2A}}{{B}}\right )^{1/5}\) | 4. | \(\left ( \dfrac{{B}}{{2A}}\right )^{1/5}\) |
Subtopic: Potential Energy: Relation with Force |
81%
Level 1: 80%+
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