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The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm², is 2 × 10¹¹ N/m². The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is 1/4 of its value on the earth. The elongation of wire is (Take g on the earth = 10 m/s²)

1. 0.1 cm
2. 0.1 mm
3. 1 mm
4. 1 cm

Correct answer: 0.1 mm

Solution

The elongation of the wire can be calculated using the formula for elongation under a tensile load, which incorporates Young's modulus, the force applied (weight of the block), the original length, and the cross-sectional area. Given that the gravitational acceleration on the planet is 1/4 of that on Earth, the effective weight of the block is reduced, resulting in a smaller elongation, which correctly leads to the answer of 0.1 mm.

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