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A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of the bullet is: (Given initial temperature of the bullet = 127°C, Melting point of the bullet = 327°C, Latent heat of fusion of lead = 2.5 × 10⁴ J kg⁻¹, Specific heat capacity of lead = 125 J/kg K)

1. 125 m s⁻¹
2. 500 m s⁻¹
3. 250 m s⁻¹
4. 600 m s⁻¹

Correct answer: 500 m s⁻¹

Solution

The correct option is right because the calculations show that the initial kinetic energy required to raise the bullet's temperature to its melting point and then provide the necessary latent heat for melting aligns with a speed of 500 m/s, which accounts for the energy conversion efficiency stated in the problem.

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