A spring 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 at the time of equilibrium is given by

Options

A. `sqrt(2) Mg`
B. `sqrt((mg)^(2)+(kx)^(2))`
C. `(sqrt((M+m)^(2)+m^(2)))g`
D. `(sqrt((M+m)^(2)+M^(2)))g`

Answer

D

Explanation

Free body diagram or pulley is shown in figure. Pulley is equilibrium under four forces. Three forces as shown in figure and the fourth, which is equal and opposite to the resultant of these three forces, is the force applied by clamp on the pulley (say F)
`R=(sqrt((M+m)^(2)+M^(2)))g`

Therefore, the force F is equal and opposite of R as shown in figure.
`F=(sqrt((M+m)^(2)+M^(2))g)`