Q. No.A force \(F\) is applied to a system of two blocks: as shown in the figure. There is no friction between the lower block and the table. Due to friction between the blocks of masses \(m\) and \(M,\) they move together through a distance \(x.\)
Then work done by \(F\) on \(m\) is:
1. \(\dfrac{Fx}{2}\)
2. \(\dfrac{m}{m+M}Fx\)
3. \(\dfrac{M}{M+m}Fx\)
4. none of the above
Two identical masses are connected to a spring of spring constant \(k.\) The two masses are slowly moved symmetrically so that the spring is stretched by \(x.\) The work done by the spring on each mass is:
1. \(\dfrac12 kx^2\)
2. \(\dfrac14kx^2\)
3. \(-\dfrac12 kx^2\)
4. \(-\dfrac14kx^2\)
| 1. | \(\dfrac{F_0}{k}\) | 2. | \(\dfrac{2F_0}{k}\) |
| 3. | \(\dfrac{4F_0}{k}\) | 4. | \(\dfrac{F_0}{2k}\) |
The kinetic energy of a particle continuously increases with time. It follows that:
| 1. | its potential energy must decrease with time |
| 2. | the net force acting on it cannot be perpendicular to its path |
| 3. | the net force acting on it is along the velocity |
| 4. | friction cannot act on it |
Given below are two statements:
| Assertion (A): | The net work done by gravity is equal to the loss in the vertical component of the kinetic energy for a projectile. |
| Reason (R): | The work-energy theorem applies to all systems including projectiles. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
| 1. | \(\dfrac{W_1}{W_2}=\dfrac mM\) | 2. | \(\dfrac{W_1}{W_2}=\dfrac hH\) |
| 3. | \(\dfrac{W_1}{W_2}=\dfrac{h}{h+H}\) | 4. | \(\dfrac{W_1}{W_2}=\dfrac 11\) |
1. \(v^{-1}\)
2. \(v^{1}\)
3. \(v^{2}\)
4. \(v^{3}\)
A small block of mass '\(m\)' is placed against a compressed spring, of spring constant \(k\). The initial compression in the spring is '\(d\)'. The block is released and the spring relaxes, while the block is projected up to a height \(H\) relative to its initial position. Then, \(H\) =
| 1. | \(\dfrac{kd^2}{2mg}\) | 2. | \(\dfrac{kd^2}{2mg}+d\) |
| 3. | \(\dfrac{kd^2}{2mg}-d\) | 4. | \(\dfrac{kd^2}{mg}+d\) |
A projectile is launched from a cliff of height \(h,\) with an initial speed \(u,\) at an angle \(\theta.\) The speed with which it hits the ground:
| 1. | depends on the vertical component, \(u \text{sin}\theta\) |
| 2. | depends on the horizontal component, \(u \text{cos}\theta\) |
| 3. | depends on \(u,\) but not on \(\theta\) |
| 4. | depends on the quantity \(u \text{tan}\theta\) |
| 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. |
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