Mass of the palnet is `1/9 of the mass of earth and its
radius is half that of the earth . IF a body weight 9 N on the earth , its weight on the planet would be

Options

A. 6 N
B. 4N
C. 2N
D. 1N

Answer

B

Explanation

Accereration fue to gravity at earth , `g_e=(GM_e)/R_e^2`
Acceleration due to gravity at planet , `g_p =(GM_p)/(R_p^2)`
`Rightarrow g_p = ((GM_e)/(9))/((R_e)/(2))^2 = (4/9) (GM_e)/(R_e)`
`g_p= 4/9 (GM_e) /(R_e^2)`
`g_p = 4/9 g_e`
therefore `("Weight on planet")/ (" weight of earth")` = `(mg_p)/(mg_e)`
`(w)'/(g) = (gp)/(g_e)` Rightarrow w' = `(4/9(g_e))/(g_e)xx w = 4/9 xx9`
therefore w' = 4N