A system of $3$ blocks is shown in figure with masses and coefficients of friction indicated in the diagram. What value of maximum horizontal force $F$ can be applied to block $B,$ so that all the three blocks have the same acceleration?

A large box is accelerated up the inclined plane with an acceleration $a_0$ and pendulum is kept vertical (Somehow by an external agent) as shown in figure. Now if the pendulum is set free to oscillate from such position. Then what is the tension in the string immediately after the pendulum is set free (mass of bob $=m$)

A block of mass $m$ is placed over smooth wedge of mass $M$ and a force $F$ is applied on wedge as shown in figure. Find minimum possible value of force $F$ so that resultant force on block $m$ becomes $mg.$

Sphere is placed between two smooth wedges, and wedges are given velocities as shown in the diagram. Velocity of centre of sphere in vertical direction will be

In the arrangement shown in figure, coefficient of friction between $4m$ and $m$ is $\mu$ and remaining all surfaces are smooth, pulleys are ideal, find minimum value of force $F$ as shown in figure, so that block $m$ remains at rest with respect to $4m.$

In the shown diagram there is no friction between $2m$ and inclined plane, while coefficient of friction between $2m$ and $m$ is $\mu .$ Maximum possible value of angle $\alpha ,$ so that there is no sliding between $2m$ and $m$

Find value of $F$ shown in the diagram so that system remains in equilibrium, all the surfaces are smooth and wedge is fixed.

A block of mass $m$ is placed over rough horizontal plank of mass $4 m$ which is placed over smooth surface as shown, find maximum value of $v_0$ so that block does not fall from the plank (length of plank is $\ell$)