$A$ body of mass $100 \ gm$ moves with a constant speed along a circular path of radius $r$. What is the work done during one complete revolution?

$A$ force of $10 \ N$ acting at an angle on a particle produces a displacement of $(3 \hat{i} - 4 \hat{\jmath}) \ m$. Due to this force,if the kinetic energy of the particle is decreased by $25 \ J$,then the angle between the force and the displacement is:

$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

$A$ simple pendulum of length $1 \,m$ has a wooden bob of mass $M = 1 \,kg$. It is struck by a bullet of mass $m = 10^{-2} \,kg$ moving with a speed of $u = 2 \times 10^2 \,m/s$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10 \,m/s^2$): (in $\,m$)

$A$ bullet fired into a fixed target loses half of its velocity after penetrating $1\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion?

Two particles $P$ and $Q$ each of mass $3m$ lie at rest on the $X$-axis at points $(-a, 0)$ and $(+a, 0)$,respectively. $A$ third particle $R$ of mass $2m$ initially at the origin moves towards the particle $Q$ with velocity $v$. If all the collisions of the system of $3$ particles are elastic and head-on,the total number of collisions in the system is