$A$ car accelerates from rest to $u \ m/s$. The energy spent in this process is $E \ J$. The energy required to accelerate the car from $u \ m/s$ to $2u \ m/s$ is $nE \ J$. The value of $n$ is ..............

$A$ ball bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

Select the incorrect statement regarding the mechanical energy of a body/system.

$A$ particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $v = \alpha \sqrt{x}$,where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x = 0$ to $x = d$ will be:

$A$ bead of mass $\frac{1}{2} \, kg$ starts from rest from point $A$ to move in a vertical plane along a smooth fixed quarter ring of radius $5 \, m$,under the action of a constant horizontal force $F = 5 \, N$ as shown. The speed of the bead as it reaches point $B$ is ................ $m/s$. [Take $g = 10 \, m/s^2$]

$A$ ball of mass $0.4 \ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.5 \ m$ while applying the force and the ball goes up to $5 \ m$ height further,find the magnitude of the force (in $N$) $(g = 10 \ m/s^2)$.