4
Question
Derive an expression for acceleration due to gravity on a plant of mass M and radius R.
Derive an expression for acceleration due to gravity on a plant of mass M and radius R.
Open in App
Solution
Consider an object of mass m lying on or near the surface of the the planet.
According to Newton's law of gravitation, the force of attraction (F) between the planet and the object is
F=GMm/R2 ...............1
According to Newton's second law of motion this force produces an acceleration (g) in the object.
F = ma (a = g)
F = mg
put value of F in equation 1
mg=GMm/R2
g=GM/R2
where
g=gravity on the planet in m/s2
G=gravitational constant
M=mass of the planet
R=radius of planet
Consider an object of mass m lying on or near the surface of the the planet.
According to Newton's law of gravitation, the force of attraction (F) between the planet and the object is
F=GMm/R2 ...............1
According to Newton's second law of motion this force produces an acceleration (g) in the object.
F = ma (a = g)
F = mg
put value of F in equation 1
mg=GMm/R2
g=GM/R2
where
g=gravity on the planet in m/s2
G=gravitational constant
M=mass of the planet
R=radius of planet
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
