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Question

A metallic ring of radius 'r', cross sectional area 'A' is fitted into a wooden circular disk 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
AYRr
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B
AY(Rr)r
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C
Y(Rr)Ar
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D
YRAr
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Solution

The correct option is B $$\dfrac{AY(R-r)}{r}$$
$$ Y = \dfrac{F/A}{\triangle l/l}$$         (standard result)
$$ F = \dfrac{Y \triangle l  A}{l}$$
$$ = \dfrac{Y (R-r) A}{r}             (\because  \triangle  l = R-r)$$

Physics

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