A balloon with mass $'m'$ is descending down with an acceleration $'a'$ (where $a < g$ ). How much mass should be removed from it so that it starts moving up with an acceleration $'a'$ ?

A body of mass $8\,kg$ is hanging another body of mass $12\,kg$. The combination is being pulled by a string $T _2$ will be respectively: (use $g =9.8\,m / s ^2$ )

Block $B$ moves to the right with a constant velocity $v_0$. The velocity of body $A$ relative to $B$ is:

Block of $3\,kg$ is initially in equilibrium and is hanging by two identical springs $A$ and $B$ as shown in figures. If spring $A$ is cut from lower point at $t=0$ then, find acceleration of block in $ms ^{-2}$ at $t =0$.

A point mass $m$ is suspended from a light thread of length $l,$ fixed at $O,$ is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are

For the equilibrium of a body on an inclined plane of inclination $45^{\circ}$. The coefficient of static friction will be