A block of mass '$m$' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance $25 \mathrm{cm}$ when, its speed is halved. The value of spring constant of used spring will be $nE \mathrm{N} {\mathrm{m}}^{-1}$ for $n=$_____.

A bullet of mass $200 \mathrm{g}$ having initial kinetic energy $90 \mathrm{J}$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40 \mathrm{J}$ within $1 \mathrm{s}$, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

An object of mass $m$ initially at rest on a smooth horizontal plane starts moving under the action of force $F=2 \mathrm{N}$. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta =kx$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $\mathrm{E}=\frac{\mathit{n}}{\mathit{k}}\sin \theta$. The value of $n$ is ______.

Identify the correct statements from the following:

(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative

(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative

(C) Work done by friction on a body sliding down an inclined plane is positive

(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero

(E) Work done by the air resistance on an oscillating pendulum is negative

Choose the correct answer from the options given below:

As per the given figure, a small ball $P$ slides down the quadrant of a circle and hits the other ball $Q$ of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball $Q$ after collision will be : $(g = 10 \mathrm{m} {\mathrm{s}}^{-2})$