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 2L and radius 2r is stretched with a force of 2F, the increase in its length will be
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a
l
b
2l
c
l2
d
l4
answer is A.
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Detailed Solution
l = FLAY = FLπr2Y ∴ l ∝FLr2 (γ = constant)∴ l2l1 = F2F1×L2L1(r1r2)2 = 2×2×(12)2 = 1∴ l2 = l1, i.e., increment in its length will be l.