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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA particle moves with uniform speed \( v \) along a circle of radius \( R \) centered at the origin in the \( xy \)-plane. The angular momentum of the particle about a point \( P(2R, 0) \) on the \( x \)-axis varies between minimum and maximum values \( L_{\min} \) and \( L_{\max} \). The ratio \( \frac{L_{\max}}{L_{\min}} \) is:
Correct answer · Option 3
3
Explanation
The distance from point P to the velocity line ranges from closest approach \( r_{\perp,\min} = 2R - R = R \) to farthest distance \( r_{\perp,\max} = 2R + R = 3R \) (at the points where velocity is perpendicular to the line joining P and the particle). Thus, \( L_{\max} = m v (3R) \) and \( L_{\min} = m v (R) \), giving \( \frac{L_{\max}}{L_{\min}} = 3 \).
