Exercise 7.4
Two objects A and B of mass m and m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?
NCERT’s answer
$\displaystyle 2$:$\displaystyle 1$
\(\displaystyle v_{A} : v_{B} = 2 : 1 \) — the lighter object moves twice as fast.
Equal kinetic energies: \(\displaystyle \frac{1}{2}m\,v_{A}^{2} = \frac{1}{2}(4m)\,v_{B}^{2} \)
Cancelling \(\displaystyle \frac{1}{2}m \): \(\displaystyle v_{A}^{2} = 4\,v_{B}^{2} \)
Taking the square root: \(\displaystyle v_{A} = 2\,v_{B} \), so the ratio is \(\displaystyle 2:1 \).