1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A test particle is moving in circular orbit in the gravitational field produced by a mass density ρ(r)=Kr2. Identify the correct relation between the radius R of the particle's orbit and its period T-

A
TR2 is a constant
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
TR is a constant
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
TR is a constant
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
T2R3 is a constant
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C TR is a constantGravitational force experienced by the test particle is given by, F=GMmr2=∫Gρ(dV)mr2 =mG∫R0kr24πr2drr2 =−4πkGm[1r]R0 =−4πkGmR Using newton's second law, we have mv20R=4πkGmR ⇒ v0=C(const.) Time period, T=2πRv0=2πRC ⇒TR=const. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (A) is the correct answer.

Suggest Corrections
36
Join BYJU'S Learning Program
Related Videos
Kepler's Law
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program