Question

A body of mass \( 30 \) kg moving with a velocity \( 20 \) ms\(^{-1}\) undergoes one-dimensional elastic collision with another ball of the same mass moving in the opposite direction with a velocity of \( 30 \) ms\(^{-1}\). After collision, the velocities of the first and second bodies respectively are:

• A. \( 25 \) ms\(^{-1}\), \( 30 \) ms\(^{-1} \)
• B. \( 30 \) ms\(^{-1}\), \( 30 \) ms\(^{-1} \)
• C. \( 30 \) ms\(^{-1}\), \( 20 \) ms\(^{-1} \)
• D. \( 40 \) ms\(^{-1}\), \( 15 \) ms\(^{-1} \)

Hint:

In an elastic collision between two bodies of the same mass, their velocities get interchanged after collision. This helps in quick calculations without using complex formulas.

Answer 1

The Correct Option is C

Step 1: Understanding Elastic Collision
For a perfectly elastic head-on collision between two bodies of equal mass, the velocities of the two objects are exchanged. The final velocities \( v_1 \) and \( v_2 \) are given by: \[ v_1 = u_2, \quad v_2 = u_1 \] where: - \( u_1 = 20 \) ms\(^{-1}\) (initial velocity of mass \( m_1 \))
- \( u_2 = -30 \) ms\(^{-1}\) (initial velocity of mass \( m_2 \))
Step 2: Applying the Elastic Collision Formula
Since both masses are equal, their velocities get interchanged: \[ v_1 = -30 \text{ ms}^{-1}, \quad v_2 = 20 \text{ ms}^{-1} \] Step 3: Conclusion
Thus, after collision, the first body moves with a velocity of \( 30 \) ms\(^{-1}\) and the second body moves with \( 20 \) ms\(^{-1}\). \[ \mathbf{30 \text{ ms}^{-1}, 20 \text{ ms}^{-1}} \]