$A$ block of mass $5 \ kg$ is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration $2 \ m/s^2$. The work done by tension on the block during the first $3 \ s$ is $(u = 0)$. (in $J$)

$A$ 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 physical quantity is conserved in both elastic and inelastic collisions?

Which of the following statements is incorrect?

$A$ train is moving along the tracks at a constant speed $u$. $A$ girl on the train throws a ball of mass $m$ straight ahead along the direction of motion of the train with speed $v$ with respect to herself. Then

$A$ $2\,kg$ block slides on a horizontal floor with a speed of $4\,m/s$. It strikes an uncompressed spring and compresses it until the block is motionless. The kinetic friction force is $110\,N$ and the spring constant is $1000\,N/m$. The spring compresses by ........ $cm$.