The mass of a body is measured on the planet Earth as M kg. When it is taken to a planet of radius half that of the Earth then its value will be
a) 4M b) 2M c) M/4 d)M
Answers
The mass of the body will be constant everywhere. So the answer is (d) M.
If it asks for weight... The answer shall be M/4 as square of the distance between the objects is inversely proportional to the weight of the body.
Given:
The mass of a body is measured on planet earth as m kg.
To find:
When it is taken to a plant of radius half that of the earth then its value will be kg
Solution:
Consider the equation of force,
F = GMm/R²
where, the attractive force (F) of two masses (m) separated at distance (R) gravitational constant (G).
mg = GMm/R²
g = GM/R² .......(1)
as the other planet has radius half that of the earth,
Thus, g' = GM/(R/2)²
g' = GM/(R²/4)
g' = 4GM/R²
g'/4 = GM/R² .......(2)
comparing equations (1) and (2), we get,
g = g'/4
mg = mg'/4
F = F'/4
Therefore, the mass of a body on a plant of radius half that of the earth is m/4.