Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

c): Initial length (circumference) of the ring $=2\pi r$

Final length (circumference) of the ring $=2\pi R$

Change in length=$2\pi R-2\pi r.$

strain=$\frac{changeinlength}{originallength}=\frac{2\pi (R-r)}{2\pi r}=\frac{R-r}{r}$

Now young's modulus $E=\frac{F/A}{t/L}=\frac{F/A}{(R-r)/r}$

$F=AE\left(\frac{R-r}{r}\right)$