Question

A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by

• A. $\sqrt{(M+m{)}^2+M^{2}g}$
• B. $\sqrt{2}Mg$
• C. $\sqrt{2}mg$
• D. $\sqrt{(M+m{)}^2+m^{2}g}$

Answer 1

The correct option is A $\sqrt{(M+m{)}^2+M^{2}g}$

$FBD$ of pulley is shown below
Let $F_{PC}$ be reaction force on pulley due to tension on string

Forces acting on pulley are self-weight, tension due to string on both sides as shown, reaction due to support hinge

$T=Mg$ as block is in equilibrium
Since pulley is in equilibrium as it fixed

$\therefore F_{PC}=\sqrt{T^2+(Mg+mg{)}^2}$

$\therefore F_{PC}=\sqrt{M{g}^2+(Mg+mg{)}^2}$

$\therefore F_{PC}=\sqrt{M^2+(M+m{)}^{2}g}$