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

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

A

0.5 cm

B

2 cm

C

4 cm

D

8 cm

Answer

4 cm

Explanation

Solution

l=FLAY⇒l∝1r2l = \frac { F L } { A Y } \Rightarrow l \propto \frac { 1 } { r ^ { 2 } } (F, L and Y are constant)

l2l1=(r1r2)2=(2)2=4\frac { l _ { 2 } } { l _ { 1 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } = ( 2 ) ^ { 2 } = 4 ⇒l2=4l1=4 cm\Rightarrow l _ { 2 } = 4 l _ { 1 } = 4 \mathrm {~cm}