Question

A body of mass M is kept on a rough horizontal surface (friction coefficient = μ). 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 A is F, where

Options

• F = Mg

• F = μ Mg

• Mg ≤ F ≤ Mga `sqrt(1+mu^2)`

• Mg ≥ F ≥ Mg `sqrt(1-mu^2)`

Answer 1

Mg ≤ F ≤ Mga `sqrt(1+mu^2)`
Let T be the force applied on an object of mass M.
If T = 0, F_min = Mg.
If T is acting in the horizontal direction, then the body is not moving.
∴ T = μ(mg)

F_max = `sqrt("Mg"^2+"T"^2)`

= `sqrt("Mg"^2+(mu"Mg")^2)`

Thus, we have:

Mg ≤ F ≤ Mga `sqrt(1+mu^2)`