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Q. No.A particle experiences a variable force \(\vec F = (4x \hat i + 3y^2 \hat j)\) in a horizontal x-y plane. Assume distance in meters and force is in newton. If the particle moves from point \((1,2)\) to point \((2,3)\) in the x-y plane, the kinetic energy changes by:
1. \(50.0\) J
2. \(12.5\) J
3. \(25.0\) J
4. \(0\)
1. \(50.0\) J
2. \(12.5\) J
3. \(25.0\) J
4. \(0\)
Subtopic: Work Energy Theorem |
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The total work done on a particle is equal to the change in its kinetic energy:
| 1. | always |
| 2. | only if the forces acting on it are conservative |
| 3. | only if gravitational force alone acts on it |
| 4. | only if elastic force alone acts on it |
Subtopic: Work Energy Theorem |
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It is given that the block never loses contact (in the figure given below) with the smooth horizontal surface, and the force always acts at an angle \(\theta\) with the horizontal. The speed of the block when it covers a horizontal distance \(l\) will be:
| 1. | \(\sqrt{\dfrac{l F_{} \cos \theta}{m}}\) | 2. | \(\dfrac{2 l \mathrm{~F}_{} \cos \theta}{\mathrm{m}}\) |
| 3. | \(\sqrt{\dfrac{2 l}{m} F_{} \cos \theta}\) | 4. | \(\dfrac{l \mathrm{~F}_{} \cos \theta}{\mathrm{m}}\) |
Subtopic: Work Energy Theorem |
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A man of mass \(m,\) standing at the bottom of the staircase, of height \(L,\) climbs it and stands at its top.
| (a) | work done by all forces on man is equal to the rise in potential energy \(mgL.\) |
| (b) | work done by all forces on man is zero. |
| (c) | work done by the gravitational force on man is \(mgL.\) |
| (d) | the reaction force from a step does no work because the point of the application of the force does not move while the force exists. |
Choose the correct option:
1. (a), (d)
2. (a), (c)
3. (b), (d)
4. (a), (b), (c)
Subtopic: Concept of Work | Work Energy Theorem |
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A force acts on a \(2\) kg object so that its position is given as a function of time as \(x = 3t^2 + 5\). What is the work done by this force in the first \(5\) seconds?
1. \(850\) J
2. \(900\) J
3. \(950\) J
4. \(875\) J
1. \(850\) J
2. \(900\) J
3. \(950\) J
4. \(875\) J
Subtopic: Work Done by Variable Force |
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A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled \(3~\text{m}\) is:
1. \(2.5~\text{J}\)
2. \(6.5~\text{J}\)
3. \(4~\text{J}\)
4. \(5~\text{J}\)
Subtopic: Work Energy Theorem |
83%
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Given below are two statements:
| Statement I: | The magnitude of the momentum of a body is directly proportional to its kinetic energy. |
| Statement II: | Kinetic energy increases whenever an external force acts on a moving body. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Concept of Work |
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A \(2\) kg particle moves along \(x\)-axis such that its position \((x)\) varies with time \((t)\) as \(x = 2t^{2}+3. \) During the initial \(5\) s, the work done by all the forces acting on the particle is:
1. \(400\) J
2. \(500\) J
3. \(600\) J
4. \(900\) J
Subtopic: Work Energy Theorem |
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The kinetic energy of a particle continuously increases with time. Then we can conclude that:
| (a) | The resultant force on the particle must be parallel to the velocity at all instants. |
| (b) | The resultant force on the particle must be at an angle less than \(90^{\circ}\) all the time. |
| (c) | Its height above the ground level must continuously decrease. |
| (d) | The magnitude of its linear momentum is increasing continuously. |
Choose the correct option:
| 1. | (a) and (b) | 2. | (b) and (c) |
| 3. | (b) and (d) | 4. | (c) and (d) |
Subtopic: Work Energy Theorem |
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A bullet when fired at a target has its velocity decreased by \(50\%\) after penetrating \(30\) cm into it. Then, the additional thickness that it will penetrate (in cm) before coming to rest is:
1. \(10\)
2. \(30\)
3. \(40\)
4. \(60\)
1. \(10\)
2. \(30\)
3. \(40\)
4. \(60\)
Subtopic: Work Energy Theorem |
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