$A$ bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into a $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3$,how far will the block slide approximately (in $,m$)?

$A$ particle $P$ is sliding down a frictionless hemispherical bowl. It passes the point $A$ at $t = 0$. At this instant of time, the horizontal component of its velocity is $v$. $A$ bead $Q$ of the same mass as $P$ is ejected from $A$ at $t = 0$ along the horizontal string $AB$ (see figure) with the speed $v$. Friction between the bead and the string may be neglected. Let ${t_P}$ and ${t_Q}$ be the respective time taken by $P$ and $Q$ to reach the point $B$. Then

$A$ block of mass $1 \ kg$ is placed at point $A$ on a rough path. It is gently pushed to the right. It slides down the slope and reaches point $B$. Find the work done by the friction force on the block during the journey from point $A$ to point $B$ in $J$. (Assume the vertical height difference between $A$ and $B$ is $0.2 \ m$ and the block starts and ends at rest).

If a lighter body (mass $M_1$ and velocity $V_1$) and a heavier body (mass $M_2$ and velocity $V_2$) have the same kinetic energy,then

Two bodies $A$ and $B$ of masses $1.5 \ kg$ and $3 \ kg$ are moving with velocities $20 \ m \ s^{-1}$ and $15 \ m \ s^{-1}$ respectively. If the same retarding force is applied on the two bodies,then the ratio of the distances travelled by the bodies $A$ and $B$ before they come to rest is

Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.