$A$ ball is allowed to fall from a height of $10 \, m$. If there is $40 \%$ loss of energy due to impact,then after one impact the ball will rise to a height of ........ $m$.

$A$ block of mass $1\,kg$ is pushed up a surface inclined to the horizontal at an angle of $30^{\circ}$ by a force of $10\,N$ parallel to the inclined surface (see figure). The coefficient of friction between the block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the incline,calculate:
$(a)$ Work done against gravity
$(b)$ Work done against the force of friction
$(c)$ Increase in potential energy
$(d)$ Increase in kinetic energy
$(e)$ Work done by the applied force

$A$ machine which is $70 \%$ efficient raises a $10 \,kg$ body through a certain distance and spends $100 \,J$ energy. The body is then released. On reaching the ground, the kinetic energy of the body will be

Explain oblique collision.

Is the statement "The work done by object $B$ on object $A$ is equal and opposite to the work done by object $A$ on object $B$" correct?

$A$ particle of mass $m$ is moving along the $x$-axis with initial velocity $u \hat{i}$. It collides elastically with a particle of mass $10m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1} = \sqrt{n} \sin \theta_{2}$,then the value of $n$ is: