Q. No.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
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 |
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. \(-mg u\)
2. \(mg u \cos\theta\)
3. \(-mgu \cos^2\theta\)
4. \(-mg u \sin\theta\)
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. \(200~\text{W}\)
2. \(250~\text{W}\)
3. \(2000~\text{W}\)
4. \(500~\text{W}\)
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
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 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 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. | \(\dfrac{kd^2}{mg}+d\) |
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