In the figure shown, the blocks have equal masses. Friction, mass of the string and the mass of the pulley are negligible. The magnitude of the acceleration of the centre of mass of the blocks is (Acceleration due to gravity = g).

Options

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

Answer

D

Explanation

For a pulley and block system on a smooth double inclined plane as shown below

Force equation for both the blocks,
`rArr mg cos 30^(@) - T = m a` …(i)
`rArr T - mg cos 60^(@) = m a` …(ii)
From above equation we get,
`a = (sqrt(3) - 1)/(4) g`
`because` Magnitude of the acceleration of centre of mass,
`a_(CM) = |(m a_(1) + m a_(2))/(m + m)|`
Here, `a_(CM) = |(((sqrt(3) -1)/(4))g hat(i) + ((sqrt(3) - 1)/(4))g hat(j))/(2)|`
`= (g)/(2) sqrt(((sqrt(3) - 1)/(4))g hat(i) + ((sqrt(3) - 1)/(4))^(2))`
`= (g)/(2) xx sqrt(2) xx (sqrt(3) - 1)/(4)`
`= ((sqrt(3) - 1)/(4sqrt(2)))g`
Hence, option (d) is correct.