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: Understanding the Concept:
A stationary body has zero momentum. After the explosion, total momentum is still zero, so the two parts have equal momentum with opposite directions.

Step 2: Key Formula or Approach:
\[ M_1V_1 = M_2V_2 = p, \qquad K = \frac{p^2}{2M} \]

Step 3: Detailed Explanation:
\[ \frac{K_1}{K_2} = \frac{p^2/2M_1}{p^2/2M_2} = \frac{M_2}{M_1} \]
The lighter fragment gets more kinetic energy.

Step 4: Check the options.
(A) is the inverse of the correct ratio. (C) and (D) are squared and do not come from \(K = p^2/2M\).

Final Answer:
The ratio \(K_1 : K_2 = M_2 : M_1\), option (B). \[ \boxed{\frac{M_2}{M_1}} \]