Question

An artificial satellite revolves around a planet for which gravitation force(F) varies with distance r from its centre as F∝ r². If v0 is its orbital speed, then
(1) v0∝ r^-1/2
(2) v0∝ r^3/2
(3) v0∝ r^-3/2
(4) v0∝ r

Answer 1

Hola User__________________

Here is Your Answer...!!
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⭐Actually welcome to the concept of the GRAVITATIONAL ANALYSIS.

⭐Basically as per the weird condition....

⭐Here the gravitational force is directly proportional to the square law ..

⭐so what do we get is ...

⭐F = GMm . r^2

⭐so we get ....

⭐mv^2/r = GMm.r^2

⭐THEREFORE. ..

⭐V° = underoot GM r^3

⭐thus V° is directly proportional to r^3/2

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Hope it helps u...☺

Answer 2

F=kr^2
where k is any constant
if body is moving in circle then it will experience a centripital force
F=(mv^2)/r
kr^2=(mv^2)/r
(kr^3)/m=v^2
v0 is directly proportional to r^3/2, where k/m is constant
hence option 2 is correct