A wire of length \( L \) and radius \( r \) is rigidly fixed at one end. On stretching the other...

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A wire of length \( L \) and radius \( r \) is rigidly fixed at one end. On stretching the other end of the wire with a force \( F \), the increase in its length is \( l \). If another wire of same material but of length \( 2 L \) and radius \( 2 r \) is stretched with a force of \( 2 F \), the increase in its length will be [NCERT 1980; AIIMS 1980;
MP PET 1992; MP PMT 2002; UPSEAT 2002;
Odisha JEE 2009; AIIMS 2010; MP PET 2013]
(a) 1
(b) 21
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{4} \)
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