A body of mass 1 kg rests on a horizontal floor with which it has a… | JEE Main 2021 (17 Mar, Shift 2)

Q17JEE Main 2021 · 17 MAR · SHIFT 2Medium

Friction Basics

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$ . It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________. (Round off to the Nearest Integer) [Take g = 10 ms ${}^{-}$ 2 ]

Numerical answer type. Work it out, then open the answer.

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Answer: 5

Pull at angle $\theta$ above horizontal: $F\cos\theta = \mu(mg - F\sin\theta) \Rightarrow F = \dfrac{\mu mg}{\cos\theta + \mu\sin\theta}$ .
Minimum when $\tan\theta = \mu$ : $F_{min} = \dfrac{\mu mg}{\sqrt{1+\mu^2}}$ .
$F_{min} = \dfrac{(1/\sqrt{3})(10)}{\sqrt{4/3}} = \dfrac{10}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{2}$
So $F = 5\text{ N}$ .

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