$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If there is no friction between any two surfaces,then:

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.

$A$ person of mass $60\, kg$ is inside a lift of mass $940\, kg$ and presses the button on the control panel. The lift starts moving upwards with an acceleration of $1.0\, m/s^2$. If $g = 10\, m/s^2$,the tension in the supporting cable is .......... $N$.

$A$ 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?

Work done by frictional force is: