Q. No.Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below:
| Statement I: | An object moves from position \(r_1\) to position \(r_2\) under a conservative force field \(\vec{F}\). The work done by the force is \(W=-\int_{r_1}^{r_2} \vec{F} \cdot d\overrightarrow{r}\). |
| Statement II: | Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. |
| 1. | Both Statement I and Statement II are True |
| 2. | Statement I is False but Statement II is True |
| 3. | Statement I is True but Statement II is False |
| 4. | Both Statement I and Statement II are False |
Subtopic: Concept of Work |
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Level 3: 35%-60%
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Which one of the following forces cannot be expressed in terms of potential energy?
| 1. | Coulomb's force | 2. | Restoring force |
| 3. | Gravitational force | 4. | Frictional force |
Subtopic: Concept of Work |
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Level 1: 80%+
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Given below are two statements:
Choose the most appropriate answer from the options given below:
| Assertion (A): | In a central force field, the work done is independent of the path chosen. |
| Reason (R): | Every force encountered in mechanics does not have an associated potential energy. |
Choose the most appropriate answer from the options given below:
| 1. | Both (A) and (R) are true, but (R) is not the correct explanation of (A) |
| 2. | (A) is false, but (R) is true |
| 3. | Both (A) and (R) are true, and (R) is the correct explanation of (A) |
| 4. | (A) is true, but (R) is false |
Subtopic: Concept of Work |
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Level 2: 60%+
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A ball having kinetic energy \(KE,\) is projected at an angle of \(60^\circ\) from the horizontal. What will be the kinetic energy of he ball at the highest point of its flight?
1. \(\dfrac{KE}{4}\)
2. \(\dfrac{KE}{16}\)
3. \(\dfrac{KE}{2}\)
4. \(\dfrac{KE}{8}\)
1. \(\dfrac{KE}{4}\)
2. \(\dfrac{KE}{16}\)
3. \(\dfrac{KE}{2}\)
4. \(\dfrac{KE}{8}\)
Subtopic: Concept of Work |
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Level 1: 80%+
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A ball of mass \(100~\text g\) is projected with a velocity of \(20~\text{m/s}\) at an angle of \(60^\circ\) above the horizontal. What is the decrease in its kinetic energy as it moves from the point of projection to the highest point of its trajectory?
1. \(20~\text{J}\)
2. \(5~\text{J}\)
3. zero
4. \(15~\text{J}\)
1. \(20~\text{J}\)
2. \(5~\text{J}\)
3. zero
4. \(15~\text{J}\)
Subtopic: Concept of Work |
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Level 2: 60%+
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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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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 |
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If the momentum of a body is increased by 20%, then its kinetic energy increases by:
1. 36%
2. 40%
3. 44%
4. 48%
1. 36%
2. 40%
3. 44%
4. 48%
Subtopic: Concept of Work |
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Level 2: 60%+
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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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Level 1: 80%+
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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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Level 1: 80%+
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