A metal ring of initial radius r and cross-sectional area A is fitted onto a wooden disc of radius R > r. If Youngs modules of metal is Y then tension in the ring is

Options

A. `(AY r)/((R-r))`
B. `(Y(R-r))/(r)`
C. `(AY(R-r))/(R)`
D. `(AY(R-r))/(r)`

Answer

D

Explanation

(d) Change in length of ring `=2piR-2pir`
Longitudinal strain `=(2piR-2pir)/(2pir)=(R-r)/(r)`
Young's , `Y=(F//A)/((R-r)/(r))`
`implies Y=(Fr)/(A(R-r))`
`implies F=(YA(R-r))/(r)`