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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 bullet is:
(Given, initial temperature of the bullet $= 127 ° C$ ,
Melting point of the bullet $= 327 ° C$ ,
Latent heat of fusion of lead $= 2.5 \times 10^{4} {JKg}^{- 1}$ ,
Specific heat capacity of lead $= 125 J / kgK$ )

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$125 m s^{- 1}$

$500 m s^{- 1}$

$600 m s^{- 1}$

$250 m s^{- 1}$

answer is B.

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Detailed Solution

$\begin{array}{rcl} m \times 125 \times 200 + m \times 2.5 \times 10^{4} & = & \frac{1}{2} {mv}^{2} \times \frac{40}{100} \\ V & = & 500 m / s \end{array}$

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