Equal force $F ( > mg)$ is applied to string in all the $3$ cases. Starting from rest, the point of application of force moves a distance of $2 m$ down in all cases. In which case the block has maximum kinetic energy?

The kinetic energy $K$ of a particle moving along $x$-axis varies with its position $(x)$ as shown in figure The magnitude of force acting on particle at $x=9 \,m$ is ............ $N$

$A$ block of mass $m$ is hung vertically from an elastic thread of force constant $mg/a$. Initially the thread was at its natural length and the block is allowed to fall freely. The kinetic energy of the block when it passes through the equilibrium position will be :

For a particle moving under the action of a variable force, kinetic energy-position graph is given, then

A $4 \,kg$ mass and a $1\, kg$ mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

A block moving horizontally on a smooth surface with a speed of $40\, {m} / {s}$ splits into two parts with masses in the ratio of $1: 2$. If the smaller part moves at $60\, {m} / {s}$ in the same direction, then the fractional change in kinetic energy is :-