Question

planet mars has radius one half that of earth and mass 1/9 of earth.find the value of 'g' on surface of earth.Given the value of 'g' on earth is 9.81m/s^2 (steps plz)

Answer 1

Acceleration due to gravity of Earth, g=(GM)/R^2= 9.81m/s^2

where M-Mass of Earth, R-Radius of Earth & G-Gravitational constant

Acceleration due to gravity of any planet, g'=(GM')/R'^2 -----------(i )

where M'-Mass of planet, R'-Radius of planet & G-Gravitational constant

To find acceleration due to gravity of any planet in comparison to earth put R'=R/2 & M'= 4M in equation (i).

We get,

Acceleration due to gravity of required planet, g'=(G4M)/(R/2)^2

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

=16 {(GM)/R^2}

g'=16g

i.e. Acceleration due to gravity of required planet=16 times acceleration due to gravity of earth

Acceleration due to gravity of required planet=16*9. 81 m/s^2

Acceleration due to gravity of required planet=156.96 m/s^2

Answer 2

from your question, it is clarity that the value of g on earth is 9.8m/s

so, can say that the value of g on the surface of earth is also 9.8 m/s².