Q 11-10-075JEE MainJEE Main 2022 (24 Jun, Shift 2)Easy
A $100\ \text{g}$ iron nail is hit by a $1.5\ \text{kg}$ hammer striking at a velocity of $60\ \text{m s}^{-1}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron $= 0.42\ \text{J g}^{-1}\,^\circ\text{C}^{-1}$]
Answer: (A) $16.07^\circ\text{C}$
Kinetic energy of the hammer $= \frac12(1.5)(60)^2 = 2700\ \text{J}$; heat to the nail $= \dfrac{2700}{4} = 675\ \text{J}$.
$$\Delta T = \frac{Q}{mc} = \frac{675}{100\times0.42} \approx 16.07^\circ\text{C}$$
Solution by Sreeraj P, M.Sc Physics