TS EAMCET · Physics · Mechanical Properties of Solids
A metallic ring of radius \(r\) and cross sectional area \(A\) is fitted into a wooden circular disc of radius \(R(R>r)\). If the Young's modulus of the material of the ring is \(Y\), the force with which the metal ring expands is
- A \(\frac{A Y R}{r}\)
- B \(\frac{A Y(R-r)}{r}\)
- C \(\frac{Y(R-r)}{A r}\)
- D \(\frac{Y R}{A R}\)
Answer & Solution
Correct Answer
(B) \(\frac{A Y(R-r)}{r}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & Y=\frac{F}{A} \cdot \frac{L}{l} \\ & \therefore \text { Force } F=\frac{A Y l}{L}=\frac{A Y[2 \pi(R-r)]}{2 \pi r} \\ & \Rightarrow \quad F=\frac{A Y(R-r)}{r}\end{aligned}\)
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