As shown in the figure , a block of mass $\sqrt{3}$ kg is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3 \sqrt{3}}$ . The critical force to be applied on the vertical surface as shown at an angle $60 °$ with horizontal such that it does not move, will be $3 x$ . The value of $x$ will be ________.
$[g = 10 m / s^{2}; \sin 60 ° = \frac{\sqrt{3}}{2}; \cos 60 ° = \frac{1}{2}]$

Question

As shown in the figure , a block of mass $\sqrt{3}$ kg is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3 \sqrt{3}}$ . The critical force to be applied on the vertical surface as shown at an angle $60 °$ with horizontal such that it does not move, will be $3 x$ . The value of $x$ will be ________.

$[g = 10 m / s^{2}; \sin 60 ° = \frac{\sqrt{3}}{2}; \cos 60 ° = \frac{1}{2}]$

Infinity Learn · Accepted Answer

In vertical direction, N−mg−Fsin⁡$$60$$∘$$=0$$⇒$$N=mg+32FandFcos60$$°$$=fNo$$ slip condition , f≤μN⇒$$F2$$≤μ$$mg+32F$$⇒$$F2$$≤$$133103+32F$$⇒$$33F$$≤$$203+3F$$⇒$$23F$$≤$$203$$⇒F≤$$10N$$⇒$$3x$$≤$$10$$⇒$$x=103=3.33$$

Friction

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Friction

Remember concepts with our Masterclasses.

In vertical direction, N−mg−Fsin⁡60∘=0⇒N=mg+32FandFcos60°=fNo slip condition , f≤μN⇒F2≤μmg+32F⇒F2≤133103+32F⇒33F≤203+3F⇒23F≤203⇒F≤10N⇒3x≤10⇒x=103=3.33

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