A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is ..............

The force constant of a wire is $k$  and that of another wire is $2k.$ When both the wires are stretched through same distance, then the work done

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled $3\, m$ is ................ $\mathrm{J}$

A particle of mass $m $ is moving in a horizontal circle of radius $r$  under a centripetal force equal to $ - K/{r^2}$, where $K$  is a constant. The total energy of the particle is

A ball is released from certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

A force of $5\, N$, making an angle $\theta $ with the horizontal, acting on an object displaces it by $0.4\,m$ along the horizontal direction. If the object gains kinetic energy of $1\,J$, the horizontal component of the force is......$N$