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?

Wedge shown in the figure is fixed. System is released from rest (Neglect friction)

Following figures show two different systems in equilibrium. The spring balance reads the tension in the string. There is no friction anywhere and pulleys are light. Select the correct alternative. ($S_1, S_2, S_3$ and $S_4$ are the readings of the balances)

In the arrangement shown, the pulleys are massless and frictionless. The rope connected to the block is also light and inextensible. The system is in equilibrium. Select the correct alternative.

A block of mass $m$ is connected with another block of mass $2m$ by a light spring. $2m$ is connected with a hanging mass $3m$ by an inextensible light string. At the time of release of block $3m$

The two arrangement of identical frictionless and massless pulleys, string and blocks are shown in figure (a) and figure (b). Which of the following statement(s) is/are correct?