A 1.0-kg mass (mA) and a 7.0-kg mass (mB) are attached to a lightweight cord that passes over a frictionless pulley. The hanging masses are free to move. Find the acceleration of the larger mass

Answer 1

a = [(mB-mA)/(mB+mA)]*g = (3/4)g

You can derive it by writing free-body motion equations for each mass, and eliminating the cord tension force, T.

mA*a = T - mA*g
mB*a = mB*g -T

(mB + mA)*a = (mB - mA)*g

Answer 2

9 m/s2