Q. No.1. \(50.0\) J
2. \(12.5\) J
3. \(25.0\) J
4. \(0\)
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 |
| 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. | \(\dfrac{l \mathrm{~F}_{} \cos \theta}{\mathrm{m}}\) |
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 from the given ones:
| 1. | (a), (d) | 2. | (a), (c) |
| 3. | (b), (d) | 4. | (a), (b), (c) |
1. \(850\) J
2. \(900\) J
3. \(950\) J
4. \(875\) J
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. \(5~\text{J}\)
| 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. |
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
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 from the given ones:
| 1. | (a) and (b) only | 2. | (b) and (c) only |
| 3. | (b) and (d) only | 4. | (c) and (d) only |
1. \(10\)
2. \(30\)
3. \(40\)
4. \(60\)
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