In the figure,a block of weight $60 \ N$ is placed on a rough surface. The coefficient of friction between the block and the surface is $0.5$. What should be the maximum weight $W$ (in $N$) such that the block does not slip on the surface?

$A$ bead of mass $m$ can slide on a frictionless fixed ring of radius $r$. With the help of two identical springs of force constant $k$,it is connected to two diametrically opposite nails $A$ and $B$,each of which is at a distance $0.5r$ from the centre $O$ of the ring. The relaxed length of each spring is negligible compared to the radius of the ring. The bead is given a small velocity. What can you predict for the further motion of the bead before any of the springs strikes a nail?

$A$ balloon of mass $m$ is descending down with an acceleration $\frac{g}{2}$. How much mass should be removed from it so that it starts moving up with the same acceleration?

An ideal spring is connected between two blocks of masses $M$ and $m$. This system can move on a smooth horizontal table. The blocks are brought closer to compress the spring and then released. In the subsequent motion,select the true statement$(s)$:
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.

Two unequal masses $A$ and $B$ moving along a straight line are brought to rest by equal retarding forces. If $A$ takes double the time taken by $B$ to come to rest and $A$ travels $\frac{2}{3}$ of the distance covered by $B$ before coming to rest,then the ratio of masses of $A$ and $B$ is . . . . . . .

$A$ $10 \, kg$ ball attached to the end of a rigid massless rod of length $L = 1 \, m$ rotates at a constant speed in a horizontal circle of radius $r = 0.5 \, m$ and period $T = 1.57 \, s$ as shown in the figure. The force exerted by the rod on the ball is ........ $N$.