Question

A body of mass m is kept on a rough horizontal surface of friction coefficientμ. A force is applied horizontally, but the body is not moving. The net force 'F' by the surface on the body will be

• A. F ≤μ mg
• B. F = μ mg
• C. mg≤ F ≤ mg $\sqrt{1 + \mu^{2}}$
• D. mg ≥ F ≥ mg $\sqrt{(1 - \mu^{2})}$

Answer 1

Answer: (C)

mg≤ F ≤ mg $\sqrt{1 + \mu^{2}}$

Answer 2

If the body is not moving, F = f, f is the force of friction on the body

and 0 ≤ f ≤ μmg or 0 ≤ F ≤ μmg . . . (i)

The force by the surface on the body

F = $\sqrt{f^{2} + R^{2}} = \sqrt{F^{2} + (mg)^{2}}$

or F = mg $\sqrt{\mu^{2} + 1}$ ∴ mg ≤ F ≤ mg $\sqrt{1 + \mu^{2}}$ ,

Hence the correct choice is