In given figure all surfaces are smooth. The ratio of forces exerted by the wedge on mass 'M' when force 'F' is not applied and when 'F' is applied such that 'M' is at rest with respect to wedge is

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$\cos^{2} θ$

$\sec^{2} θ$

1 : 2

answer is D.

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Detailed Solution

F not applied N -mg cos $θ$
F applied $N^{1} = masin θ + mgcos θ$
$\begin{array}{l} N^{1} = mgtan θsin θ + mgcos θ \\ = mg \frac{(\sin^{2} θ + \cos^{2} θ)}{\cos θ} \\ \frac{N}{N^{1_{}}} = \frac{\cos^{2} θ}{1} \end{array}$

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