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

Options

A. `sqrt2mg`
B. `sqrt2mg`
C. `[sqrt((M + m)^(2) + m^(2))]g`
D. `[sqrt((M + m)^(2) + m^(2))]g`

Answer

c

Explanation

Force on the pulley by the clamp = resultant of `T = (M + m)` g and mg acting along horizontal and vertical directions respectively
`= sqrt([(M + m) g]^(2) + (mg)^(2))`
`=[sqrt((M + m)^(2) + m^(2)]]g` .