Q 11-10-055JEE MainJEE Main 2025 (23 Jan, Shift 1)Easy
A gun fires a lead bullet of temperature $300\ \text{K}$ into a wooden block. The bullet, having melting temperature of $600\ \text{K}$, penetrates into the block and melts down. If the total heat required for the process is $625\ \text{J}$, then the mass of the bullet is ______ grams. (Latent heat of fusion of lead $= 2.5\times10^4\ \text{J kg}^{-1}$ and specific heat capacity of lead $= 125\ \text{J kg}^{-1}\text{K}^{-1}$)
Answer: (A) $10$
Heat to warm the bullet to its melting point and then melt it:
$$Q = m(s\Delta T + L) = m(125\times300 + 2.5\times10^4) = m(37500 + 25000) = 62500\,m$$
$$62500\,m = 625 \Rightarrow m = 0.01\ \text{kg} = 10\ \text{g}$$
Solution by Sreeraj P, M.Sc Physics