Q. No.A body of mass \(m\) starts moving from rest along the \(x\text{-axis}\) so that its velocity varies as \(v = a \sqrt s\) where \(a\) is a constant and \(s\) is the distance covered by the body. The total work done by all the forces acting on the body in the first \(t\) seconds after the start of the motion is:
1. \(8ma^4 t^ 2\)
2. \(\frac{1} {4} ma^4 t^ 2\)
3. \(4ma^4 t ^2\)
4. \(\frac{1} {8} ma^4 t^ 2\)
1. \(8ma^4 t^ 2\)
2. \(\frac{1} {4} ma^4 t^ 2\)
3. \(4ma^4 t ^2\)
4. \(\frac{1} {8} ma^4 t^ 2\)
Subtopic: Concept of Work |
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Level 2: 60%+
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Two particles of the same mass \(m\) are moving in circular orbits because of force given by \(F(r) =\left( \frac{-16}{r}-r^3\right). \) The first particle is at a distance \(r = 1 \) and the second at \(r = 4. \) The best estimate for the ratio of kinetic energies of the first and the second particle is closest to:
1. \(3\times 10^-3\)
2. \(6\times 10^2\)
3. \(6\times 10^{-2}\)
4. \( 10^{-1}\)
1. \(3\times 10^-3\)
2. \(6\times 10^2\)
3. \(6\times 10^{-2}\)
4. \( 10^{-1}\)
Subtopic: Concept of Work |
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Level 2: 60%+
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Two solids \(A\) and \(B\) of mass \(1\) kg and \(2\) kg respectively are moving with equal linear momentum. The ratio of their kinetic energies \((KE)_A:(KE)_B\) will be:
1. \(1:2\)
2. \(2:1\)
3. \(1:4\)
4. \(4:1\)
Subtopic: Concept of Work |
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Level 2: 60%+
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Two particles having masses \(4\) g and \(16\) g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is \(n : 2\). The value of \(n\) will be:
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
Subtopic: Concept of Work |
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Level 1: 80%+
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Given below are two statements:
| Statement I: | A truck and a car moving with equal kinetic energy are stopped by an equal retarding force. Both will cover equal distances to stop. |
| Statement II: | A car moving towards the east suddenly changes its direction towards the north with the same speed. In this case, its acceleration will be zero. |
| 1. | Both Statement I and Statement II are True. |
| 2. | Both Statement I and Statement II are False. |
| 3. | Statement I is True and Statement II is False. |
| 4. | Statement I is False and Statement II is True. |
Subtopic: Concept of Work |
52%
Level 3: 35%-60%
JEE
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A particle which is experiencing a force, given by; \(\vec{F}=(3\vec{i}- 12\vec{j}), \) undergoes a displacement of \(\vec d=4\hat{i}\) If the particle had a kinetic energy of \(3~ \text J \) at the beginning of the displacement, what is its kinetic energy at the end of the displacement?
1. \(9 ~\text J \)
2. \(12 ~\text J \)
3. \(10 ~\text J \)
4. \(15 ~\text J \)
1. \(9 ~\text J \)
2. \(12 ~\text J \)
3. \(10 ~\text J \)
4. \(15 ~\text J \)
Subtopic: Concept of Work |
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A boy is rolling a \(0.5 ~\text{kg}\) ball on the frictionless floor with a speed of \(20~\text{m/s}.\) The ball gets deflected by an obstacle on the way. After deflection, it moves with \(5\%\) of its initial kinetic energy. What is the speed of the ball now?
1. \(14.41~\text{m/s}\)
2. \(19.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
4. \(4.47~\text{m/s} \)
1. \(14.41~\text{m/s}\)
2. \(19.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
4. \(4.47~\text{m/s} \)
Subtopic: Concept of Work |
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A body at rest is moved along a horizontal straight line by a machine delivering constant power. The distance moved by the body in time \('t’\) is proportional to:
1. \(\large t^{\frac{3}{4}}\)
2. \(\large t^{\frac{3}{2}}\)
3. \(\large t^{\frac{1}{2}}\)
4. \(\large t^{\frac{1}{4}}\)
1. \(\large t^{\frac{3}{4}}\)
2. \(\large t^{\frac{3}{2}}\)
3. \(\large t^{\frac{1}{2}}\)
4. \(\large t^{\frac{1}{4}}\)
Subtopic: Concept of Work |
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Two persons \(A\text{ and }B\) perform the same amount of work in moving a body through a certain distance \({d}\) with the application of forces acting at angle \({45^\circ~\text{and}~60^\circ}\) with the direction of displacement respectively. The ratio of force applied by a person \({A}\) to the force applied by a person \(B~\text{is}~\frac{1} {\sqrt{x}}.\) The value of \({x}\) is:
1. \(4\)
2. \(7\)
3. \(5\)
4. \(2\)
1. \(4\)
2. \(7\)
3. \(5\)
4. \(2\)
Subtopic: Concept of Work |
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Identify the correct statements from the following.
Choose the correct answer from the options given below:
| \(\mathrm{A}.\) | Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. |
| \(\mathrm{B}.\) | Work done by the gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. |
| \(\mathrm{C}.\) | Work done by friction on a body sliding down an inclined plane is positive. |
| \(\mathrm{D}.\) | Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero. |
| \(\mathrm{E}.\) | Work done by the air resistance on an oscillating pendulum is negative. |
| 1. | \(\mathrm{B}\) and \(\mathrm{E}\) only | 2. | \(\mathrm{A}\) and \(\mathrm{C}\) only |
| 3. | \(\mathrm{B}\) and \(\mathrm{D}\) only | 4. | \(\mathrm{B},\) \(\mathrm{D}\) and \(\mathrm{E}\) only |
Subtopic: Concept of Work |
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Level 2: 60%+
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