Two blocks A and B of equal masses are attached to a string passing over a smooth pulley fixed to a wedge as shown in figure. Find the magnitude of acceleration of centre of mass of the two blocks when they are released from rest. Neglect friction.

Options

A. `((sqrt(3)-1)/(4sqrt(2))g)`
B. `(sqrt(3)-1)g`
C. `g/2`
D. `((sqrt(3)-1)/(sqrt(2)))g`

Answer

A

Explanation

Acceleration of system,
`a=(mg sin 60-mg sin 30)/(2m)`
`a=((sqrt(3)-1)/4) g`, Now `bar(a)_(cm)=(mbar(a)_(1)+mbar(a)_(2))/(2m)`
here `bar(a)_(1)` and `bar(a)_(2)` are `((sqrt(3)-1)/4)g` at right angles
hence, `a_(cm)=(sqrt(2)a)/2=((sqrt(3)-1)/(4sqrt(2)))g`