COMEDK · Physics · 10. Mechanical Properties of Solids
A force \(F\) applied on the wire of radius \(r\) and length \(L\) and change in the length of the wire is l. If the same force \(F\) is applied on the wire of the same material and radius \(4 r\) and length \(4 l\), then change in length of the other wire is,
- A \(\dfrac{l}{4}\)
- B \(2 l\)
- C \(\dfrac{l}{2}\)
- D \(4 l\)
Answer & Solution
Correct Answer
(A) \(\dfrac{l}{4}\)
Step-by-step Solution
Detailed explanation
Young's modulus \(Y\) is defined as \(Y = \dfrac{F L}{A l}\), where \(A = \pi r^2\) is the cross-sectional area of the wire. For the first wire, \(Y = \dfrac{F L}{(\pi r^2) l}\). For the second wire, let the change in length be \(l'\). The material is the same, so \(Y\) remains…
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