A small block starts slipping down from a point \(B\) on an inclined plane \(AB,\) which is making an angle \(\theta\) with the horizontal. Section \(BC\) is smooth and the remaining section \(CA\) is rough with a coefficient of friction \(\mu\). It is found that the block comes to rest as it reaches the bottom (point \(A\)) of the inclined plane. If \(BC = 2AC,\) the coefficient of friction is given by \(\mu=k\tan\theta\). The value of \(k\) is:
           
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)

A particle of mass \(m\) is moving along the\(x\)-axis with an initial velocity \(u\hat{i}.\) It undergoes an elastic collision with another particle of mass \(10m,\) which is initially at rest. After the collision, the first particle retains half of its initial kinetic energy (as shown in the figure). If \(\sin \theta_1=\sqrt{n} \sin \theta_2,\) then the value of \(n\) is:
            
1. \(5\)
2. \(10\)
3. \(15\)
4. \(20\)

A cricket ball of mass \(0.15~\text{kg}\) is thrown vertically up by a bowling machine so that it rises to a maximum height of \(20~\text{m}\) after leaving the machine. If the part pushing the ball applies a constant force \(F\) on the ball and moves horizontally a distance of \(0.2~\text{m}\) while launching the ball, the value of \(F\) (in N) is: (\(g = 10\) m/s²)
1. \(50\)
2. \(100\)
3. \(150\)
4. \(200\)

A particle moves unidirectionally on a horizontal plane, under a constant power-supplying energy source. The displacement-time \((s\text-t)\) graph that describes the motion of the particle is:
(graphs are drawn schematically and are not to scale)

1.		2.
3.		4.

A block of mass \(1.9~\text{kg}\) is at rest at the edge of a table, of height \(1~\text{m}\). A bullet of mass \(0.1~\text{kg}\) collides with the block and sticks to it. If the velocity of the bullet is \(20\) m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is: [Take \(g = 10\) m/s² . Assume there is no rotational motion and loss of energy after the collision is negligible.]
1. \(21~\text{J}\)
2. \(23~\text{J}\)
3. \(20~\text{J}\)
4. \(19~\text{J}\)

A body of mass \(2\text{ kg}\) is driven by an engine delivering constant power \(1~\text{J/s}. \) The body starts from rest and moves in a straight line. After \(9\text{ s}, \) the kinetic energy of the body is:
1. \(4.5~\text{J}\)
2. \(9~\text{J}\)
3. \(13.5~\text{J}\)
4. \(18~\text{J}\)

Blocks with masses \(m,2m,4m\) and \(8m\) are arranged in a line on a frictionless floor. Another block of mass \(m,\) moving with speed \(v\) along the same line (see figure) collides with the first stationary block of mass \(m\) in a perfectly inelastic collision. All subsequent collisions are also perfectly inelastic. By the time the last block of mass \(8m\) starts moving, the total energy loss is \(p\%\) of the original energy. The value of \(p\) is closest to:

Two particles of masses \(4\) g and \(16\) g have equal kinetic energies. If the ratio of the magnitudes of their linear momenta is \(n : 2,\) what is the value of \(n\)?
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)

A particle is moving along a circular path with a radius \(a,\) under the influence of an attractive force. The potential energy associated with the particle is given by: \(U=-\dfrac{k}{2r^2}.\)
The attractive force acting on the particle is:

In a collinear collision, a particle with an initial speed \(v_0\) strikes a stationary particle of the same mass. If the final total kinetic energy is \(50\%\) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:
1. \(\frac{{v_0}}{4}\)
2. \(\sqrt{2}{v_0}\)
3. \(\frac{{v_0}}{2}\)
4. \(\frac{{v_0}}{\sqrt{2}}\)