Question

If the radius of the earth is to shrink by 1% (mass remains the same) the acceleration due to gravity g on the Earth's surface will increase by how much % ?

Answer 1

The acceleration due to gravity g = GM/r2 = 9.8 m/s2 If r reduces by 1%, the new radius becomes r' = 99% of r = 99r/100 = 0.99r New acceleration due to gravity g' = GM/(0.99r)2 = GM/(0.98r2 ) = 1.04 g = 10.19 m/s2 Increase in acceleration due to gravity = 10.19 − 9.8 m/s2 = 0.39 m/s2 Increase in percentage = 0.39 x 100/9.8 = 3. 97%

Answer 2

g=GM/r^2

g=1/r^2. g"=1/r"^2.

r"=r- •01r

r"=•99r

g"/g=r^2/(•99r)^2

g"/g=1/•9801

g"=g/•9801

g(final)-g(initial)×100/g(initial)

(g/•9801-g)×100/g(initial)

g increases by 2%