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Question

A metal ring of initial radius r and cross-sectional area A is fitted onto a wooden disc of radius R>r .if Young's modulus of metal is Y then tension in the ring is:


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Solution

Step 1. Given data:

Metal ring of radius = r

Cross-sectional area = A

Wooden ring radius = R

Young modulus of metal = Y

Step 2. Formula used:

We know, Young's modulus of the metal Y=σε, where σ=stress, ε=strain.

ε=strain.= ∆lL, ∆l=change in length, L=original length, stress σ=TA, where T=tension, A=cross-sectional area.

Step 3. Calculations:

ε=∆lL=2πR-2πr2πr=R-rr

Thus, Y=σε=TAR-rrT=AYR-rr

Hence, the tension in the ring is AYR-rr.


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