OnlineCBT
Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीTwo stars of equal mass \( M \) revolve in circular orbits of radius \( R \) about their common centre of mass under mutual gravitational attraction. If the orbital speed of each star is \( v \), what would be the new orbital speed of each star if the separation between them is halved, keeping their circular orbits about the centre of mass?
Correct answer · Option 4
\( \sqrt{2}v \)
Explanation
Separation is \( 2R \). Gravitational force \( F = \frac{GM^2}{(2R)^2} = \frac{Mv^2}{R} \implies v = \sqrt{\frac{GM}{4R}} \). If separation is halved to \( 2R' = R \implies R' = R/2 \), then \( v' = \sqrt{\frac{GM}{4(R/2)}} = \sqrt{2}v \).
