Two blocks `A` and `B` each of equal masses `m` are rleased from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the accelertion of the centre of mass of the two blocks.

Explanation

Let us consider incline surfaces of wedge as `x`-axis and `y`-axis respectively. We can write accelerations of blocks `A` and `B`.

`veca_(A)=mg sin 30^(@) hati` and `veca_(B)=mg cos 30^(@)hatj`
The acceleration of centre of mass of two blocks can be written as
`veca_(cm)=(m_(A)veca_(A)+m_(B)veca_(B))/(m_(A)+m_(B))=(mgsin30^(@)hati+mgsin60^(@)hatj)/(m+m)`
`(gsin30^(@)hati+gsin60^(@)hatj)/2`
`=g/4hati+(sqrt(3)g)/4hatjimplies |veca_(cm)|=g/2`