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 bullet is ............ \(ms ^{-1}\) (Given, initial temperature of the bullet \(=127^{\circ} C\), Melting point of the bullet \(=327^{\circ} C\), Latent heat of fusion of lead \(=2.5 \times 10^{4} \,J Kg ^{-1}\), Specific heat capacity of lead \(=125 \,J / kg K\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.