$A$ neutron makes a head-on elastic collision with a stationary deuteron. The fractional loss of energy of the neutron in this collision is:

Consider an elastic collision of a particle of mass $m$ moving with velocity $u$ with another particle of the same mass $m$ at rest. After the collision, the particles move at angles $\theta_1$ and $\theta_2$ with respect to the initial direction of motion. What is the sum of the angles $\theta_1 + \theta_2$ in degrees?

The bob $A$ of a pendulum,released from a horizontal position to the vertical,hits another bob $B$ of the same mass at rest on a table as shown in the figure. If the length of the pendulum is $1\,m$,calculate:
$(a)$ The height to which bob $A$ will rise after the collision.
$(b)$ The speed with which bob $B$ starts moving.
Neglect the size of the bobs and assume the collision to be elastic.

$A$ light particle moving horizontally with a speed of $12\ m/s$ strikes a very heavy block moving in the same direction at $10\ m/s$. The collision is one-dimensional and elastic. After the collision,the particle will

$A$ ball of mass $2m$ and a system of two balls with equal masses $m$ connected by a massless spring are placed on a smooth horizontal surface (see figure). Initially, the ball of mass $2m$ moves with velocity $u_0$ along the line passing through the centres of all the balls and the spring, whereas the system of two balls is at rest. Assuming that the collision between the individual balls is perfectly elastic, the ratio of vibrational energy stored in the system of two connected balls to the initial kinetic energy of the ball of mass $2m$ is

$A$ particle of mass $m$ moving with velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a very short time $T$. Their force of interaction increases from zero to $F_0$ linearly in time $T/2$, and decreases linearly to zero in further time $T/2$. The magnitude of $F_0$ is