The ratio of the weights of a body on Earth’s surface to that on the surface of a planet is 9 : 4 The…

The ratio of the weights of a body on Earth’s surface to that on the surface of a planet is 9:4 The mass of the planet is 19th of that of the Earth. If R is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density)
  1. R4
  2. R2
  3. R3
  4. R9

Solution

Weight =mGMR2
∴94=GMeRe2×Rp2GMp
Given that, Mp=Me9
∴94=MeMe9×Rp2Re2
Rp2=Re2×14
Rp=Re2
As, Re=R
⇒Rp=R2

Asked in: JEE Main 2019 (12 Apr Shift 2)

Practice more Gravitation questions on Aicharya