Question

A body of mass M is kept on a rough horizontal surface (friction coefficient = $\mu$). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is F, where

• A. F = Mg
• B. F = $\mu$Mg
• C. Mg $\le$ F $\le$ Mg $\sqrt{1+{\mu }^2}$
• D. Mg $\ge$ F $\ge$ Mg $\sqrt{1+{\mu }^2}$

Answer 1

The correct option is C

Mg $\le$ F $\le$ Mg $\sqrt{1+{\mu }^2}$

If $F_1$ = 0

So contact force will only have Normal which is equal to Mg
So F will be Mg

Now as $F_1$ increases fr keeps increasing till it reaches limiting value i.e., $\mu$N = $\mu$ mg
So, in that case, contact force F will be

$\sqrt{N^2+{f_r}^2}$ = $\sqrt{{\left(Mg\right)}^2+{\left(\mu Mg\right)}^2}$

F = Mg $\sqrt{1+{\mu }^2}$

This means contact force F will lie between Mg $\le$ F $\le$ Mg $\sqrt{1+{\mu }^2}$