KVPY SX SB Exam 20141 Question Paper

Consider the system shown below.
A horizontal force F is applied to a block X of mass 8 kgsuch that the block Y of mass 2 kg adjacent to it does notslip downwards under gravity. There is no friction betweenthe horizontal plane and the base of the block X. Thecoefficient of friction between the surfaces of blocks X andY is 0.5. Take acceleration due to gravity to be 10 ms${}^{-2}$.
The minimum value of F is