Question 96 of 210

A block of mass $200g$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F=\sqrt{x}N$ as shown in figure.

The value of x=_____.

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Answer: 12

Balancing the forces in horizontal direction $N\sin \theta =F$
And balancing the forces in vertical direction $N\cos \theta =mg$
$\Rightarrow \tan \theta =\dfrac{F}{mg}$$\Rightarrow F=mg\tan \theta$
$F=0.2\times 10\times \sqrt{3}=\sqrt{12}N$. Therefore, $x=12$

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