Question

A thin steel ring of inner radius \(r\) and cross-sectional area \(A\) is fitted on to a wooden disc of radius \(R(R>r)\). If Young's modulus be \(Y\), then the tension in the steel ring is \(AY((R-r)/nr)\). Find \(n\).

Answer 1

Inner radius of ring \(=r\)
Outer radius of ring \(=R\)
Strain,

\(\dfrac{\Delta l}{l}=\left(\dfrac{2\pi R-2\pi r}{2\pi r}\right)\)

\(\Rightarrow \dfrac{\Delta l}{l}=\left(\dfrac{R-r}{r}\right)\)

\(Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}\)

\(\Rightarrow Y\dfrac{\Delta l}{l}A=F\)

\(\Rightarrow F=AY\left(\dfrac{R-r}{r}\right)\)


Final Answer: \(1\)