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

Answer 1

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

The FBDs of the block and pulley are


Since, the entire system is in equilibrium, force applied by the clamp will be the resultant of $T$ and $(mg+T)$
But, from the FBD of block, $T=Mg$


$\therefore$ Force applied by clamp
$=\sqrt{(Mg{)}^2+(mg+Mg{)}^2}$
$=g\sqrt{M^2+(M+m{)}^2}$