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 blocks.

`a=(mg(sin 60^(@)-sin 30^(@)))/(m+m)`
`=(g)/(2)((sqrt(3))/(2)-(1)/(2))=(g)/(4)(sqrt(3)-1)`
`vec(a)_(cm)=(m[a cos 60^(@)hat(j)]+masin 60^(@)(-hat(i))+m(a cos 60^(@))hat(j))/(m+m)`
`=(ma)/(2m)[[(-1)/(2)-(sqrt(3))/(2)]hat(i)+((1)/(2)-(sqrt(3))/(2))hat(j)]`
`(a)/(4)[-(1+sqrt(3))hat(i)+(1-sqrt(3))hat(j)]`
`a_(cm)=(a)/(4)sqrt([(1+sqrt(3))hat(i)+(1-sqrt(3))hat(j)])=`
`(a)/(4)sqrt(1+3+2sqrt(3)+1-2sqrt(3)+3)=(a)/(4)sqrt(8)`
`=(a)/(4)2sqrt(2)=(a)/(sqrt(2))a_(cm)=(g)/(4sqrt(2))(sqrt(3)-1)`