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 $\ell$)

Consider the shown arrangement. All pulleys are massless and strings are ideal. Coefficient of friction between block $A$ and surface is $\mu =0.5. \text{A}$ force $F$ is applied on $A$ so that block $C$ does not move. Then the value of $F,$ is. (Given mass of each block $A, B$ and $C$ are $1 \mathrm{kg}$)

A block of mass $M$ is placed on a horizontal surface. It is tied with an inextensible string that passes through ideal pulleys. A mass $m$ is connected to the pulley as shown. For what value of $m,$ the block $M$ will accelerate towards the fixed pulley?

An arrangement of pulleys and blocks is shown in the figure. The two pulleys and the strings are ideal. If $m_2>m_1,$ then which of the following(s) is/are wrong?