A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms⁻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 Jg⁻¹ °C⁻¹]

Solution

Physics sir · 4 steps

Find the hammer's kinetic energy, take one fourth of it as heat, then use Q = mc Δ T for the nail.

1. Hammer's energy. The hammer's kinetic energy is 1/2Mv² = 1/2 × 1.5 × 60² = 2700 J.
2. Heat into nail. One fourth of this heats the nail, so Q = 2700/4 = 675 J.

   Δ T = Q/mc = 675/(100 × 0.42)

3. Match the units. The specific heat is given per gram, so keep the nail's mass as 100 g. Then mc = 42 J °C⁻¹, and Δ T = 675/42 = 16.07 °C.
4. So. The nail's temperature rises by about 16.07 °C, which is option (c).

The idea to keep. In mechanical-to-heat questions, set the fraction of energy that turns into heat equal to mc Δ T. Always match the mass unit to the unit in the specific heat.

Answer from the NTA final answer key. Solution by PrepWiser.