The linear momentum of a body of mass $8 \ kg$ is $24 \ kg \ m \ s^{-1}$. If a constant force of $24 \ N$ acts on the body in the direction of motion of the body for a time of $3 \ s$,then the increase in the kinetic energy of the body is (in $J$)

On complete combustion,a litre of petrol releases heat equivalent to $3 \times 10^7 \, J$. In a test drive,a car weighing $1200 \, kg$ (including the driver) travels $15 \, km$ per litre while moving at a uniform speed on a straight track. Assuming that the friction offered by the road surface and air is uniform,calculate the force of friction acting on the car during the test drive,given that the efficiency of the car engine is $0.5$. (in $, N$)

In two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3: 1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Then,the ratio between the relative velocity of approach and the relative velocity of separation in the second collision is:

$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

$A$ block of mass $m = 5 \text{ kg}$ is released from the top of an inclined plane as shown in the figure. The inclined plane has a length of $10 \text{ m}$ and an angle of $30^{\circ}$. The horizontal surface has a coefficient of kinetic friction $\mu = 0.5$ and a length of $2 \text{ m}$ before the spring of spring constant $k = 100 \text{ N/m}$. Calculate the maximum compression $x$ in the spring.

Two identical blocks $A$ and $B$,each of mass $m$,resting on a smooth horizontal floor,are connected by a light spring of natural length $L$ and spring constant $K$. $A$ third block $C$ of mass $m$,moving with a speed $v$ along the line joining $A$ and $B$,collides with $A$. The maximum compression in the spring is: