$A$ block of mass $1\,kg$ is suspended by a string of mass $1\,kg$ and length $1\,m$ as shown in the figure. Given $g = 10\,m/s^2$,calculate the tension in the string at its mid-point. (in $,N$)

One end of a light string is fixed to a clamp on the ground and the other end passes over a fixed frictionless pulley as shown in the figure. It makes an angle of $30^{\circ}$ with the ground. The clamp can tolerate a vertical force of $40 \,N$. If a monkey of mass $5 \,kg$ were to climb up the rope,then the maximum acceleration in the upward direction with which it can climb safely is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

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

$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If the string $C$ is stretched slowly,then

Two bodies of mass $6 \ kg$ and $4 \ kg$ are tied to a string as shown in the adjoining figure. If the table and pulley are frictionless,then the acceleration of the $6 \ kg$ mass will be $........ \ ms^{-2}$ $\left(g=10 \ ms^{-2}\right)$.

The breaking stress of a wire going over a smooth pulley is $2 \times 10^9\, N/m^2$. What would be the minimum radius of the wire used if it is not to break? (Assume $g = 10\, m/s^2$)