JEE Main 2022 — Thermal Properties of Matter Question with Solution

If we heat-up an object, then, the energy is used to either change the temperature of the body or to change the state of the body.
If it changes the temperature, then,

$Q = mS∆T$
where, $Q$ is the heat given, $m$ is the mass and $∆T$ is the change in temperature.

We know that a moving object has an energy in the form of kinetic energy, i.e.,
$KE=\frac{1}{2}m{v}^2$

When that moving object strikes another object, it loses some energy which changes into the heat energy and this heat energy increases the temperature of the object.
Given a hammer of $1.5 \mathrm{kg}$ is moving with $60 \mathrm{m} {\mathrm{s}}^{-1}$.
Kinetic energy $=\frac{1}{2}m{v}^2 = \frac{1}{2}(1.5) (60{)}^2 = 2700 \mathrm{J}$
One-fourth of kinetic energy changes into heat energy.
$\Rightarrow \frac{1}{4}\left(KE\right) =$ Heat energy
$\Rightarrow \frac{1}{4}\left(KE\right) = m\left(S\right)(∆T)$
$\Rightarrow \frac{1}{4}\left(2700\right) =\left(100\right) (0.42) (∆T)$
$\Rightarrow ∆T=16.07°\mathrm{C}$