Question

The mass of the body is measured on planet Earth as M kg. When it is taken to a planet of radius half that of the earth then it's value will be

Answer 1

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.