Under the same load, wire A having length 5 . 0 m and cross section 2 . 5 × 10 - 5 m 2 stretches uniformly by the same amount as another wire B of length 6 . 0 m and a cross section of 3 . 0 × 10 - 5 m 2 stretches. The ratio of the Young's modulus of wire A to that of wire B will be:

Question

Under the same load, wire A having length 5 . 0 m and cross section 2 . 5 × 10 - 5 m 2 stretches uniformly by the same amount as another wire B of length 6 . 0 m and a cross section of 3 . 0 × 10 - 5 m 2 stretches. The ratio of the Young's modulus of wire A to that of wire B will be:, 1 : 4, 1 : 1, 1 : 10, 1 : 2

MARKS App · Accepted Answer

Elongation in uniform wire under load is given by, Δ l = F l S Y , where S is area of cross-section. As F is same for both wire and Δ l is also same, we can write Δ l F = l S Y ⇒ l A S A Y A = l B S B Y B ⇒ 5 2 . 5 × 10 - 5 × Y A = 6 3 × 10 - 5 × Y B ⇒ Y A Y B = 1

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