Question

If two balls of the same metal weighing $5\text{gm}$ and $10\text{gm}$ strike a target with the same velocity and the heat energy developed in the balls after striking is used for raising their temperatures, then the temperature will be

• A. higher for bigger ball
• B. higher for smaller ball
• C. equal for both the balls
• D. None of the above

Answer 1

The correct option is C equal for both the balls

Let us assume, change in temperature in a ball is $\Delta T$ and $c$ is the specific heat capacity of the metal.
We know that,
Heat produced $\left(H\right)=mc\Delta T$.
From the data given in the question, by using work-energy theorem, we can say that,
$\frac{1}{2}m{v}^2=mc\Delta T$
$\Rightarrow \Delta T\propto v^2$
Hence, we can conclude that temperature does not depend on the mass of the balls, but only depends on the speed of the balls before striking the target.
Thus, option (c) is the correct answer.