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Q.

A hollow cylinder of inner radius 3 cm and outer radius 5 cm and a solid cylinder of radius 2 cm are subjected to the same force. If they are made of same material and of same length, then the ratio of their elongations is

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a

1:3

b

1:4

c

1 : 1

d

1:2

answer is C.

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Detailed Solution

$e \propto \frac{1}{r^{2}}$ $(∵ Y = \frac{F l}{A e})$

$\frac{e_{1}}{e_{2}} = \frac{r_{2}^{2}}{r_{1}^{2}} = \frac{4}{5^{2} - 3^{2}} = \frac{4}{16} = \frac{1}{4}$

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A hollow cylinder of inner radius 3 cm and outer radius 5 cm and a solid cylinder of radius 2 cm are subjected to the same force. If they are made of same material and of same length, then the ratio of their elongations is