In the figure shown, a particle of small mass m is joined to a very heavy mass M (M >> m) by a light string passing over a light pulley. The total downward force on the pulley by the string is :

Options

A. (a)mg
B. (b)2 mg
C. (c)4 mg
D. (d)(M + m) g

Answer

C

Explanation

m moves upwards with acceleration `a = ((M -m)g)/((M + m)) = ((1 - (m)/(M))/(1 +(m)/(M)))g`,
`M gt gt m implies (m)/(M) = 0`
`:. A = g` T - mg = ma = mg `implies T = 2mg`
Downward force on pulley by string = 2T = 4 mg