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A body of mass M is hung from the lower end of a metal wire whose upper end is fixed, producing an elongation l. Which statement(s) about energy is/are correct? (A) The loss in gravitational potential energy of M is M*g*l. (B) The elastic potential energy stored in the wire is M*g*l. (C) The elastic potential energy stored in the wire is (1/2)*M*g*l. (D) The heat produced is (1/2)*M*g*l.

1. (A) Loss in gravitational potential energy of M is M*g*l
2. (B) The elastic potential energy stored in the wire is M*g*l
3. (C) The elastic potential energy stored in the wire is (1/2)*M*g*l
4. (D) Heat produced is (1/2)*M*g*l

Correct answer: (A) Loss in gravitational potential energy of M is M*g*l

Solution

The mass descends by l so it loses M*g*l of gravitational PE; the wire (with force rising linearly from 0 to Mg) stores only (1/2)*M*g*l, and the remaining (1/2)*M*g*l is lost as heat — so statements A, C, D are individually correct, with A being the unambiguous loss in gravitational PE.

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