A body of mass m is placed on a rough surface with coefficient of friction `mu` inclined at `theta`. If the mass is in equilibrium , then

Options

A. `theta = tan^(-1) mu`
B. `theta = tan^(-1) (1/mu)`
C. `theta = tan^(-1) m/mu`
D. `theta = tan^(-1) mu/m`

Answer

A

Explanation

In case of limiting condition , F `=mg sin theta " " …(i)`
Normal force , R `=mg cos theta " "…(ii)`
Now, comparing eqs. (i) and (ii) we get
`F/R = (mg sin theta)/(mg cos theta) " " (therefore " force of friction, " F=muR)`
`mu = tan theta rArr theta = tan^(-1) (mu)`