A steel ring of radius r and cross-sectional area A is fitted into a

1.	A steel ring of radius r and cross-sectional area A is fitted into a wooden disc of radius R (R > r). If Young's modulus be Y, find the force with which the steel ring is expanded.
Answer» Original length, L = 2πr Extension, ΔL = 2πR - 2πr = 2π(R - r) Strain, ΔL/L = 2π(R - r)/2πr = (R - r)/r Young's modulus, Y = {(F/A)}/{(R - r)/r} or, F = YA(R - r/r)

A steel ring of radius r and cross-sectional area A is fitted into a wooden disc of radius R (R > r). If Young's modulus be Y, find the force with which the steel ring is expanded.

Answer»

Original length, L = 2πr

Extension, ΔL = 2πR - 2πr = 2π(R - r)

Strain, ΔL/L = 2π(R - r)/2πr = (R - r)/r

Young's modulus, Y = {(F/A)}/{(R - r)/r}

or, F = YA(R - r/r)