Q. No.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.
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 \(u \text{tan}\theta\) |
A particle of mass '\(m\)' is released from the origin, and it moves under the action of a force: \(F(x)= F_0-kx\)
The maximum speed of the particle is, \(v= \)
| 1. | \(\sqrt{\dfrac{F_0^2}{mk}}\) | 2. | \(\sqrt{\dfrac{2F_0^2}{mk}}\) |
| 3. | \(\sqrt{\dfrac{F_0^2}{2mk}}\) | 4. | \(2\sqrt{\dfrac{F_0^2}{mk}}\) |
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
1. \(200~\text{W}\)
2. \(250~\text{W}\)
3. \(2000~\text{W}\)
4. \(500~\text{W}\)
A force \(2x\hat i - 3y^2\hat j\) acts on a particle when it is at the location \(({x, y}).\) This force is:
| 1. | non-conservative |
| 2. | conservative and the potential energy is \(({x^2-y^3})\) |
| 3. | conservative and the potential energy is \(({y^3-x^2})\) |
| 4. | conservative, but it cannot have a potential energy |
1. \(-mg u\)
2. \(mg u \cos\theta\)
3. \(-mgu \cos^2\theta\)
4. \(-mg u \sin\theta\)
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. \(-\dfrac14kx^2\)
When a fan is switched on and it begins to rotate:
| 1. | Its K.E. increases |
| 2. | Work is done by centrifugal force |
| 3. | Work is done by centripetal forces |
| 4. | Mechanical forces do not do any work |
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