Question

A stationary body explodes into two parts of masses \(M_1\) and \(M_2\). They move in opposite directions with velocities \(V_1\) and \(V_2\). The ratio of their kinetic energies is

• A. \(\frac{M_1}{M_2}\)
• B. \(\frac{M_2}{M_1}\)
• C. \(\frac{M_1^2}{M_2^2}\)
• D. \(\frac{M_2^2}{M_1^2}\)

Hint:

Momentum is conserved and starts at zero, so the fragments have equal and opposite momenta.

Answer 1

The Correct Option is B

Step 1: Write velocities.
From $M_1V_1 = M_2V_2$, $V_1/V_2 = M_2/M_1$.

Step 2: Kinetic energy ratio.
\[ \frac{K_1}{K_2} = \frac{M_1V_1^2}{M_2V_2^2} = \frac{M_1}{M_2}\cdot\frac{M_2^2}{M_1^2} = \frac{M_2}{M_1} \]

Final Answer:
Option (B). \[ \boxed{\frac{M_2}{M_1}} \]