Question

A ball of mass m is thrown upward and another ball of same mass is thrown downward so as to move freely under gravity. The acceleration of centre of mass is

Answer 1

The acceleration of centre of mass of both bodies will be same...
Because acceleration g is always constant for all bodies...

Answer 2

Answer: the centre of mass is moving with g acceleration

Explanation:

a (centre of mass) = [m1 (vector a1 ) + m2 (vector a2)] / ( m1 + m2 )

a (centre of mass) = ( ma + ma ) / m + m

a (centre of mass) = g cause a=g which is gravity

Mass is given to be same for both the bodies