When a certain weight is suspended from a long uniform wire, its length increases by one cm. If same

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8.Mechanical Properties of Solids

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When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be ........ $cm$

A

$0.5 $

B

$2$

C

$4$

D

$8$

Solution

(c)$l = \frac{{FL}}{{AY}} \Rightarrow l \propto \frac{1}{{{r^2}}}$ $(F, L$ and $Y$ are constant)

$\frac{{{l_2}}}{{{l_1}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = {(2)^2} = 4$

$ \Rightarrow {l_2} = 4{l_1} = 4cm$

Standard 11

Physics

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