$A$ bullet of mass $30 \,g$ moving with $700 \,ms^{-1}$ collides with a block of mass $4 \,kg$ hanging by a string of length $0.4 \,m$. After the collision, the block rises to a height of $0.2 \,m$. Find the velocity of the bullet when it emerges from the block. (in $\,ms^{-1}$)

$A$ 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:

$A$ ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $x$-axis,hits another ball of mass $20\, kg$ which is at rest. After the collision,the first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along the $y$-axis with a speed of $10 \, m/s$. The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x$-axis. The velocity of the ball moving at $30^{\circ}$ with the $x$-axis is $x \, m/s$. The configuration of pieces after the collision is shown in the figure. The value of $x$ to the nearest integer is:

Which of the following statements is incorrect?

$A$ man of mass $80 \ kg$ goes to the market on a scooter of mass $100 \ kg$ with a certain speed. On application of brakes, the stopping distance is $S_1$. The man returns home on the same scooter, with the same speed with a $60 \ kg$ bag of rice. If $S_2$ is the new stopping distance when the brakes are applied with the same force, then:

$A$ ball of mass $m$ falls vertically to the ground from a height $h_1$ and rebounds to a height $h_2$. The change in momentum of the ball on striking the ground is