$A$ man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same between the man and the ground,and between the block and the ground.

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction,the magnitude of the minimum additional force needed is ........... $N$.

$A$ bullet of mass $0.1\,kg$ moving horizontally with speed $400\,m/s$ hits a wooden block of mass $3.9\,kg$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20\,m$ before coming to rest. The coefficient of friction between the block and the surface is $........$ (Given $g=10\,m/s^2$)

If an explosion occurs in a projectile,which force acts on its centre of mass?

$A$ metallic block of mass $20 \ kg$ is dragged with a uniform velocity of $0.5 \ ms^{-1}$ on a horizontal table for $2.1 \ s$. The coefficient of kinetic friction between the block and the table is $0.10$. What will be the maximum possible rise in temperature of the metal block if the specific heat of the block is $0.1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$ (in $^{\circ} C$)? Assume $g = 10 \ ms^{-2}$ and a uniform rise in temperature throughout the whole block. [Ignore absorption of heat by the table]

$A$ truck of mass $M$ is at rest on a frictionless road when a monkey of mass $m$ starts moving on the truck in the forward direction. If the truck recoils with a speed $v$ backward on the road,with what velocity is the monkey moving with respect to the truck?