Two masses $m_1 = 5\, kg$ and $m_2 = 4.8\, kg$ tied to a string are hanging over a light frictionless pulley. The acceleration of the masses when they are free to move is $...........\, m/s^2$. $(g = 9.8\, m/s^2)$

In the case of a wire having negligible mass,suspended from a ceiling and stretched under the action of a weight $F$ suspended from its other end,the tension at any cross-section of the wire is

$A$ light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs on the other side. It makes an angle of $30^{\circ}$ with the ground. $A$ monkey of mass $5 \ kg$ climbs up the rope. The clamp can tolerate a vertical force of $40 \ N$ only. The maximum acceleration in the upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10 \ m/s^2$).

$A$ loop of light inextensible string passes over smooth small pulleys $A$ and $B$. Two masses $m$ and $M$ are attached to the points $O$ and $C$ respectively. The condition that $m$ and $M$ will cross each other (given $AB = 2l$ and $AC = BC = \eta l$) is:

In the adjoining figure,the tension in the string connecting blocks $A$ and $B$ is:

In the arrangement shown in the figure,the pulleys are massless and frictionless,and the threads are inextensible. The block of mass $m_1$ will remain at rest,if