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A boy of mass M is applying a horizontal force to slide a box of mass M' on a rough horizontal force to slide coefficient of friction between the shoes of the boy and the floor is $μ$ and that between the box and the floor is $μ$ ' . In which of the following cases it is certainly not possible to slide the box ?

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$μ < μ', M < M'$

$μ > μ', M < M'$

$μ < μ', M > M'$

$μ > μ', M > M'$

answer is A.

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Detailed Solution

It will not be possible to slide the box if the maximum frictional force that can act on the box is greater than the maximum frictional force that can act on the man.

$f_{\max, man} = μMg and f_{\max, box} = μ' M' g$

$If μ < μ' and M < M', then f_{\max, man} < f_{\max, box}$

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