Acceleration due to gravity on the surface of the Earth is `9.8 m s^(-2)`. Find its new vallue if both the radius and mass increase by 20%.

Explanation

Take the mass and radius of the Earth as `M_(o) and R_(o)`. The acceleration due to gravity as `g_(o) = 9.8 m s^(-2)`
Now, when the mass and radius of the Earth both increase by 20%, then acceleration due to gravity would become `'g_(1)'`.
Take the new mass and radius of the Earth as `'M_(1)' and 'R_(1)'`.
But, `g_(0) = (GM_(o))/(R_(o)^(2))`
and `R_(1) = (120R_(o))/(100)=(6)/(5)R_(0)`,
`M_(1) = (120)/(100)M_(0) = (6)/(5) M_(0)`
`g_(1) = (GM_(1))/(R_(1)^(2))=(G xx (6)/(5)M_(0))/(((6)/(5)) xx R_(o)^(2))=(5)/(6) xx 9.8 = 8.16 m s^(-2)`