Consider the system shown below a horizontal force \( F \) is applied to a block \( X \) of mass...

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Consider the system shown below a horizontal force \( F \) is applied to a block \( X \) of mass \( 8 \mathrm{~kg} \) such that the block \( Y \) of mass \( 2 \mathrm{~kg} \) 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 \( 0.5 \). Take acceleration due to gravity to be \( 10 \mathrm{~ms}^{-2} \). The minimum value of \( F \) is
[KVPY 2014]
(a) \( 200 \mathrm{~N} \)
(b) \( 160 \mathrm{~N} \)
(c) \( 40 \mathrm{~N} \)
(d) \( 240 \mathrm{~N} \)
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