Question

If the work done in stretching a wire by 1 mm is 2J, the work necessary for stretching another wire of same material but with double radius of cross section and half the length by 1 mm is:

(a) 16 J

(b) 8 J

(c) \(\frac{1}{16}\) J

(d) \(\frac{1}{8}\) J

Answer 1

Correct option is : (a) 16 J

 \(W = \frac{1}{2}Y\frac{(\Delta l^2)A}{l}\)

For same Y and ∆l.W ∝ \(\frac{\pi r^2}{l}\)

∴ \(\frac{W_2}{W_1} = \frac{(2r)^2}{r^2}.\frac{l}{l/2} = 8\)

⇒ W₂ = 8W₁ = 8 x 2 = 16 J