If the mass of block $B$ is $3\,kg$ and the mass of block $A$ is $7\,kg$,then the acceleration of the system is ........... $m/s^2$. $(g = 10\,m/s^2)$

$A$ frictionless pulley is attached to one arm of a balance and a string passed around it carries two masses $m_1$ and $m_2$. The pulley is provided with a clamp due to which $m_1$ and $m_2$ do not move with respect to each other. On removing the clamp,if the counter mass restores balance,then the acceleration of the centre of mass of the masses $m_1$ and $m_2$ will have a magnitude of?

$A$ $4 \text{ kg}$ mass is suspended as shown in the figure. All pulleys are frictionless and the spring constant $K$ is $8 \times 10^3 \text{ Nm}^{-1}$. The extension in the spring is $\left(g=10 \text{ ms}^{-2}\right)$.

$A$ 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:

Two blocks of masses $m$ and $2m$ are connected by a metal wire of negligible mass and having cross-sectional area $A$,passing over a smooth fixed pulley as shown in the figure. If the masses are released from rest,then the stress produced in the wire is:

$A$ uniform rope of mass $M$ and length $L$ is fixed at its upper end vertically from a rigid support. The tension in the rope at a distance $l$ from the rigid support is: