Question

The mass of a body is measured on planet earth as m kg. When it is taken to a plant of radius half that of the earth then its value will be kg

Answer 1

Answer:

Same

Explanation:

In the whole time and space mass of body will never change. Only weight of body will change with gravity as weight = mg

g is acceleration due to gravity on that planet

Answer 2

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.