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

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 given figure,two masses $m_1$ and $m_2$ $(m_2 > m_1)$ are at rest in an equilibrium position. Find the tension in string $AB$.

Two masses $m_1 = 10 \ kg$ and $m_2 = 6 \ kg$ are attached to a string which passes over a frictionless smooth pulley. The acceleration of the masses is .......... $m/s^2$. (Take $g = 10 \ m/s^2$)

$A$ lift of mass $1000\,kg$ is moving with an acceleration of $1\,m/s^2$ in the upward direction. The tension developed in the cable connected to the lift is ........... $N$ $(g = 9.8\,m/s^2)$.

$A$ uniform chain of length $2L$ is hanging in an equilibrium position. If end $B$ is given a slightly downward displacement,the imbalance causes an acceleration. Here,the pulley is small and smooth,and the string is inextensible. Find the velocity $v$ of the chain when it slips out of the pulley (height of pulley from floor $> 2L$).