question_answer

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                       [IIT-JEE 2001]

A) \[\sqrt{2}Mg\] 

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

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

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

Correct Answer: D

Solution :

    Force on the pulley by the clamp             \[{{F}_{pc}}=\sqrt{{{T}^{2}}+{{[(M+m)g]}^{2}}}\]             \[{{F}_{pc}}=\sqrt{{{(Mg)}^{2}}+{{[(M+m)g]}^{2}}}\]             \[{{F}_{pc}}=\sqrt{{{M}^{2}}+{{(M+m)}^{2}}}g\]