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A uniform heavy rod of weight 10 kg m s⁻², cross-sectional area 100 cm² and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 × 10¹¹ N m⁻². Neglecting the lateral contraction, find the elongation of rod due to its own weight.

1. 1 × 10⁻⁹ m
2. 5 × 10⁻⁸ m
3. 4 × 10⁻⁸ m
4. 5 × 10⁻¹⁰ m

Correct answer: 5 × 10⁻¹⁰ m

Solution

The elongation of the rod due to its own weight can be calculated using the formula for elongation under uniform load, which incorporates the weight of the rod, its length, cross-sectional area, and Young's modulus. The correct option reflects the calculated elongation based on these parameters, confirming that the rod stretches a small amount under its own weight.

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