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Question: When a weight of 10 kg is suspended from a copper wire of length 3 metres and diameter 0.4 mm, its l...

When a weight of 10 kg is suspended from a copper wire of length 3 metres and diameter 0.4 mm, its length increases by 2.4 cm. If the diameter of the wire is doubled, then the extension in its length will be

A

9.6 cm

B

4.8 cm

C

1.2 cm

D

0.6 cm

Answer

0.6 cm

Explanation

Solution

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

l2l1=(r1r2)2=(12)2⇒l2=l14=2.44\frac { l _ { 2 } } { l _ { 1 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } = \left( \frac { 1 } { 2 } \right) ^ { 2 } \Rightarrow l _ { 2 } = \frac { l _ { 1 } } { 4 } = \frac { 2.4 } { 4 } ⇒l2=0.6 cm\Rightarrow l _ { 2 } = 0.6 \mathrm {~cm}