question_answer

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

A) \[\sqrt{2}\text{ Mg}\]

B) \[\sqrt{2}\text{ mg}\]

C) \[\sqrt{{{\left( M+m \right)}^{2}}+{{m}^{2}}}\text{ g}\]

D) \[\sqrt{{{\left( M+m \right)}^{2}}+{{M}^{2}}}\text{ g}\]

Correct Answer: D

Solution :

[d] At equilibrium \[T=Mg\] F.B.D. of pulley \[{{F}_{1}}=\left( m+M \right)g\] The resultant force on pulley is \[F=\sqrt{F_{1}^{2}+{{T}^{2}}}\] \[F=\sqrt{{{\left( m+M \right)}^{2}}+{{M}^{2}}}g\]