Consider the system shown below. A horizontal force $F$ is applied to a block $X$ of mass $8 \,kg$, such that the block $Y$ of mass $2 \,kg$ adjacent to it does not slip downwards under gravity. There is no friction between the horizontal plane and the base of the block $X$. The coefficient of friction between the surfaces of blocks $X$ and $Y$ is $0.5$. The minimum value of $F$ is ............ $N$ (take, acceleration due to gravity to be $10 \,ms ^{-2}$ )
KVPY 2014, Medium
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