$A$ ball of mass $1\,kg$ moving with a velocity of $4\,m/s$ collides with a stationary ball of mass $M$. The collision is oblique. After the collision,the first ball moves at a right angle to its initial direction with a velocity of $3\,m/s$. The momentum of the second ball (in $kg\cdot m/s$) after the collision would be nearly:

$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

$A$ lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it,the initial speed of the bullet is ............ $m \, s^{-1}$.
(Given: Initial temperature of the bullet $= 127^{\circ} C$,
Melting point of the bullet $= 327^{\circ} C$,
Latent heat of fusion of lead $= 2.5 \times 10^{4} \, J \, kg^{-1}$,
Specific heat capacity of lead $= 125 \, J \, kg^{-1} K^{-1}$)

Statement $(I)$: The slope of the kinetic energy-displacement curve of a body in motion is directly proportional to its acceleration.
Statement $(II)$: From a height of $15 \ m$, a ball is projected vertically upwards with a velocity of $30 \ m/s$. If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is $30 \%$.
Statement $(III)$: The velocity acquired by a body of mass '$m$' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass '$m$'.
Which of the following is correct?

$A$ block of mass '$m$' moving on a frictionless horizontal surface collides with a spring of spring constant '$K$' and compresses it through a distance '$x$'. The maximum momentum of the block after collision is

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 $J$)