$A$ block of mass $m$ starts at rest at height $h$ on a frictionless inclined plane. The block slides down the plane,travels across a rough horizontal surface with coefficient of kinetic friction $\mu$,and compresses a spring with force constant $k$ a distance $x$ before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface,sliding up the plane. The block travels a total distance $d$ on the rough horizontal surface. The correct expression for the maximum height $h'$ that the block reaches on its return is

$A$ block of mass $M = 1 \ kg$ is released from rest at the top of a smooth track of radius $R = 40 \ m$. The block slides along the track without toppling,and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point $Q$ (where the radius makes an angle of $30^{\circ}$ with the horizontal),as shown in the figure,is $150 \ J$. (Take the acceleration due to gravity,$g = 10 \ m s^{-2}$)
$1.$ The speed of the block when it reaches the point $Q$ is:
$(A) 5 \ m s^{-1}$ $(B) 10 \ m s^{-1}$ $(C) 10\sqrt{3} \ m s^{-1}$ $(D) 20 \ m s^{-1}$
$2.$ The magnitude of the normal reaction that acts on the block at the point $Q$ is:
$(A) 7.5 \ N$ $(B) 8.6 \ N$ $(C) 11.5 \ N$ $(D) 22.5 \ N$
Give the answers for question $1$ and $2$.

$A$ ball is dropped from a height of $20 \, cm$. The ball rebounds to a height of $10 \, cm$. What is the percentage loss of energy? ................ $\%$

$A$ constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k} \text{ N}$ causes a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k} \text{ m}$ in $2 \text{ s}$. The work done and the power are respectively:

$A$ small block of mass $200 \ g$ is placed on a horizontal slab at a height of $2 \ m$ above the floor. The block is pressed against a horizontal spring fixed at one end to compress the spring by $10.0 \ cm$. Upon releasing,the block moves horizontally until it leaves the spring. Calculate the horizontal distance covered by the block after leaving the slab and just before hitting the ground. The spring constant is $50 \ N \ m^{-1}$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)

$A$ wooden block of mass $M$ is suspended by a string. $A$ bullet of mass $m$ passes through the block with velocity $v$ and emerges with a velocity $v/2$ in the same direction. To what height will the block rise?