Question

On a surface of a planet of radius R and mass M the acceleration due to gravity is 7m/s?. Consider another planet of radius 2R and mass 0.4M. What would the acceleration due to gravity be on this new planet? Show your calculations.

Answer 1

0.7 m/
`s^(2)`

Step-by-step explanation:

From Newton's law of universal gravitation,

F =
`(GMm)/(r^(2) )`

and from Newton's second law of motion,

F = mg

So that;

mg =
`(GMm)/(r^(2) )`

⇒ g =
`(GM)/(r^(2) )`

For the first planet,

7 =
`(GM)/(R^(2) )`

⇒ G =
`(7R^(2) )/(M)` .............. 1

For the second planet,

g =
`(0.4GM)/((2R)^(2) )`

=
`(0.4GM)/(4R^(2) )`

⇒ G =
`(4gR^(2) )/(0.4M)` ............. 2

Equating 1 and 2, we have;

`(7R^(2) )/(M)` =
`(4gR^(2) )/(0.4M)`

g =
`(7R^(2) *0.4M)/(4R^(2)M )`

=
`(7*0.4)/(4)`

=
`(2.8)/(4)`

g = 0.7

Therefore, the acceleration due to gravity on the new planet is 0.7 m/
`s^(2)`.