Question

A particle of mass \( m \) is rotating in a horizontal circle of radius \( r \) with uniform velocity \( \mathbf{V} \). The change in its momentum at two diametrically opposite points will be:

• A. \( \mathbf{mV} \)
• B. \( 3mV \)
• C. \( -2mV \)
• D. \( -mV \)

Hint:

For rotational motion, the change in momentum when the velocity changes direction is calculated by considering the magnitude and direction of the velocity vectors.

Answer 1

The Correct Option is C

Step 1: Change in Momentum.
At two diametrically opposite points, the velocity vectors of the particle will have opposite directions. Therefore, the change in momentum will be: \[ \Delta \mathbf{p} = 2mV \quad (\text{since momentum is mass times velocity}) \] The negative sign indicates the reversal in direction. Step 2: Conclusion.
Thus, the change in momentum at the two points is \( -2mV \).