As shown in the figure, a block of mass 3 kg is kept on a horizontal rough surface of coefficient of friction 133. The critical force to be applied on the vertical surface as shown at an angle 60o with horizontal such that it does not move, will be __.

From the condition of equilibrium f=Fcos 600N=mg+Fsin600For no movement of the block 1MFcos600≤F⇒Fcos600≤μmg+Fsin600⇒F≤μmgcos600−μsin600⇒Fcritical=10N

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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^o with horizontal such that it does not move, will be __.

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answer is 10.

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Detailed Solution

From the condition of equilibrium $f = F \cos 60^{0}$

$N = m g + F \sin 60^{0}$

For no movement of the block $\frac{1}{M}$

$F \cos 60^{0} \leq F \Rightarrow F \cos 60^{0} \leq μ (m g + F \sin 60^{0}) \Rightarrow F \leq \frac{μ m g}{\cos 60^{0} - μ \sin 60^{0}}$

$\Rightarrow F_{c r i t i c a l} = 10 N$

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