Two blocks A and B of mass 6kg and 3kg respectively are placed on a smooth surface of an elevator in such a way that B is placed above A.The coefficient of friction between the two blocks is 1/4 and the elevator is ascending up with acceleration g/3.A horizontal force 10N is applied on A. Find the accelerations of the blocks w.r.t. the elevator.

Since,the elevator is acc upwards the value of normal will change. N-mg=mg/3 N=4mg/3=4*3*9.8/3=39.2N This is the normal force between the blocks. Now check wether the blocks will slip or not. The common acc between the two blocks is 10/3+6=10/9m/s2 Force required by B to move with common acc in horizontal direction=3*10/9=10/3N Limiting friction=coefficient of friction*normal reaction=1/4*39.2=9.8N Since,9.8 is greater than 10/3,the blocks will not slip. So, the common acc of the blocks with respect to the elevator will be equal to10/9m/s2 Along the x-axis