A cable breaks if stretched by more than 2 mm. It is cut into two equal parts. How much either part can be stretched without breaking? (A) 0.25 m (B) 0.5 mm (C) 1 mm (D) 2 mm

The elongation ΔL of a metallic cable of young modulus E, cross sectional area A and length L under the tensile load P is given by


ΔL ∝ L

Elongation ΔL is directly proportional to L, keeping P, A and E constant

From above proportionality, we have

ΔL2/ΔL1 = L2/L1

Since the cable of length L1 having elongation ΔL1 = 2 mm is broken into two equal parts

Hence, each part have now a length L2 = L1/2 i.e half the original length

Therefore, the elongation ΔL2 of each part under same tensile load P

ΔL2/2 = (L1/2)/L1

ΔL2/2 = 1/2

ΔL2 = 2/2 = 1

Therefore, each part is stretched by 1mm

So, the correct option is (C)

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