The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.5 \; m$,what is the speed (in $m/s$) with which the bob arrives at the lowermost point,given that it dissipated $5 \%$ of its initial energy against air resistance?

$A$ ball of mass $1 \ kg$ moving with a velocity of $0.4 \ m/s$ collides with another ball of the same mass at rest. After the collision,the first ball moves with a velocity of $0.3 \ m/s$ in a direction perpendicular to the initial direction. Find the magnitude of the momentum $\vec{P}$ of the second ball in $kg \cdot m/s$.

The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

$A$ ball is dropped from a height of $5\,m$ onto a sandy floor and penetrates the sand up to $1\,m$ before coming to rest. The retardation of the ball in sand (assuming it to be uniform) will be ................ $m/s^2$.

$A$ man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as

Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into