If the radius of the earth be increased by a factor of `5`, by what factor its density be changed to keep the value of `g` of the same?

Options

A. `1//25`
B. `1//5`
C. `1//sqrt(5)`
D. 5

Answer

B

Explanation

`g=(GM)/(R^(2))rArr g=(Grhpxx(4)/(3)pi R^(2))/(R^(2))rArr g=(4)/(3)pi GR rho` ….(i)
`g' = (4)/(3)pi G(5R)rho'` ….(ii)
given that `g=g'`, so `rho'=(rho)/(5)`