Question

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

• A. Mg
• B. $\frac{Mg}{2}$
• C. $\frac{Mg}{\sqrt{2}}$
• D. $Mg\sqrt{2}$

Answer 1

The correct option is D $Mg\sqrt{2}$

An ideal pulley is a frictionless and massless pulley.
At equilibrium, tension in the string,
T = Mg
Net force on clamp by pulley:
$F_p=\sqrt{T^2+T^2+2T\times T\times cos{90}^{\circ }}(\because \theta ={90}^{\circ }$
$\Rightarrow F_p=\sqrt{(Mg{)}^2+(Mg{)}^2}=\sqrt{2}Mg$
Since the system is at rest, the clamp also applies force of same magnitude on the pulley in opposite direction as that of $F_p,i.e.,F_c=Mg\sqrt{2}$
Hence, the correct answer is option (4).