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.

Two blocks A and B each of equal masses m are rleased from the top of

1.	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.
Answer» Solution :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`