The position $x$ of a particle moving along the $x$-axis at time $t$ is given by the equation $t = \sqrt{x} + 2$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first $4 \ s$ is .............. $J$.

$A$ 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

The inclined surfaces of two movable wedges of same mass $M$ are smoothly conjugated with the horizontal plane as shown in the figure. $A$ washer of mass $m$ slides down the left wedge from a height $h$. To what maximum height will the washer rise along the right wedge? Neglect friction.

$A$ small disc of mass $m$ slides down with initial velocity zero from the top $(A)$ of a smooth hill of height $H$ having a horizontal portion $(BC)$ as shown in the figure. If the height of the horizontal portion of the hill is $h$,then the maximum horizontal distance covered by the disc from the point $D$ is

Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

$A$ raindrop of mass $1.00 \, g$ falling from a height of $1 \, km$ hits the ground with a speed of $50 \, m s^{-1}$. Calculate
$(a)$ the loss of $PE$ of the drop
$(b)$ the gain in $KE$ of the drop
$(c)$ Is the gain in $KE$ equal to loss of $PE$? If not,why?
Take $g = 10 \, m s^{-2}$.