A steel ring of radius r and cross section area A is fitted on to a wooden disc of radius `R(Rgtr)`. If Young's modulus be R, then the force with which the steel ring is expanded is

Options

A. `A Y (R )/(r )`
B. `Ay((R-r)/(r ))`
C. `(Y)/(A)((R-r)/(r ))`
D. `(Yr)/(AR)`

Answer

B

Explanation

The extension in the steel ring is `2pi(R-r)`
strain `=(2pi(R-r))/(2pi r)=(R-r)/(r )`
Stress `=y xx` Strain
`therefore F=Ay xx (R-r)//r`