8) The mass of a body is measured on 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)
4 M
_kg
c) M/4
b)
2M
d) M
Answers
Answer:
d option is correct answer
Explanation:
When a body is taken to a planet of radius half that of the earth then the mass of the body is M because the mass does not change from place to place. So, the mass of the body will be constant everywhere
Given that, the mass of a body which is measured on planet Earth is 'M'.
Let us assume that the radius of the earth is 'R'.
According to Law of Gravitation,
(The force between any two objects having mass M and m is directly proportional to their masses and inversely proportional to square of distance between them.)
F = (GMm)/R²
[ F = mg ]
mg = (GMm)/R²
g = GM/R² ...................(1st equation)
As per given condition, “When it is taken to a planet of radius half that of the Earth.”
Now,
mg' = (GMm)/(R/2)²
g' = GM/(R²/4)
g' = 4GM/R²
g'/4 = GM/R²
Using (1st equation)
g'/4 = g
Or we can say that,
F'/4 = F
OR
Case 1:
F = GMm/R² ........(1st equation)
Case 2:
F' = GMm/(R/2)²
F' = GMm/(R²/4)
F' = 4GMm/R²
F'/4 = GMm/R² .....(2nd equation)
On comparing (1st equation) and (2nd equation) we get,
F'/4 = F
But as said above Force is directly proportional to mass and inversely proportional to radius. And as there is no change in mass of the body. So, the mass of the other planet is M.
Option d) M