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. `AER//r`
B. `AE(R-r)//r`
C. `E(R-r)//Ar`
D. `E r//AR`

Answer

B

Explanation

Here, young's modulus = E
change in length of ring
`Delta l=2pi R-2pi r=2 pi(R-r)`
Longituidinal strain `=(Delta l)/(l)=(2pi(R-r))/(2pi r)=(R-r)/(r)`
As, `F=YA (Delta l)/(l)= (EA(R-r))/(r)`