दो ग्रहों की त्रिज्याएँ `R_(1)`, और `R_(2)`, हैं तथा उनके घनत्व `rho_(1)` और `rho_(2)` हैं । उनकी सतहों पर गुरुत्वीय त्वरणों का अनुपात होगा -

Options

A. `(g_(1))/(g_(2))=(rho_(1))/(R_(1)^(2)).(rho_(2))/(R_(2)^(2))`
B. `(g_(1))/(g_(2))=(R_(1)R_(2))/(rho_(1)rho_(2))`
C. `(g_(1))/(g_(2))=(R_(1)rho_(1))/(R_(2)rho_(2))`
D. `(g_(1))/(g_(2))=(R_(1)rho_(2))/(R_(2)rho_(1)).`

Answer

C

Explanation

`g=(GM)/(R^(2))=(G(4)/(3)piR^(3)rho)/(R^(2))=(4)/(3)piGR rho`
`therefore (g_(1))/(g_(2))=(R_(1)rho_(1))/(R_(2)rho_(2)).`