$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

$A$ body of mass $4 \ kg$ is moving with a momentum of $8 \ kg \ m/s$. $A$ force of $0.2 \ N$ acts on it in the direction of motion for $10 \ s$. The increase in kinetic energy in joules is:

$A$ ball is dropped vertically downwards from a height $h$ above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance,which of the following graphs represents the variation between speed $(v)$ and height $(h)$ correctly?

$A$ man throws a ball to a height of $12 \ m$,where it reaches with a speed of $12 \ m/s$. If the man throws the ball such that it just reaches this height,what percentage of energy would he have saved?

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to observer $B$,the potential energy of the spring increases:

Two identical $5\,kg$ blocks are moving with the same speed of $2\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide,stick together,and come to rest. Considering the two blocks as a system,the work done on the system by the external forces will be ............. $Joule$.