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If work done for stretching a wire by 1 mm is 2 J, then the work necessary for stretching another wire of same material, but with double the radius and half the length by 1 mm (in Joule) is 
  1. 16
  2. 8 
  3. 4 
  4. 1


Solution

The correct option is A 16
The work done in stretching a wire is defined as,
W=AYl22L=πr2Yl22L
Here 
r is radius of the wire
L is length of the wire
l is extension of the wire
Y is Youngs Modulus

Wr2L
W1W2=r21(r2)2×L2L1
W1W2=r21(2r1)2×L1/2L1
W1W2=18
W2=8W1

Given,
W1=2 J
W2=16 J

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