GATE-2018 (24) :Wyllie – Time average equation

106. A planet is 11 times the radius of the Earth in size, but one-fourth in mass density. The gravity field on its surface would be around (in gals)

A) 1600

B) 2700

C) 3300

D) 3500

Solution:

Earth radius = r_E

Planet radius = r_p = 11* r_E

Earth density = ρ_E

Planet density = ρ_P = ρ_E /4

Gravity of the planet g_P = G m / r² -------------(1)

Desnity = Mass / Volume

Mass = Density * Volume

       = (4/3 * Π * r³ * ρ)

Substitute above values in eq (1)

g_p = (G * 4/3 * П * r³ * ρ) / r²

g_p = (G * 4/3 * П * r * ρ)

g_p = (6.67*10^-11 * 4/3 * 3.14 * 11* 6371000* 1/4 *5500) km /s²

g_p =322 /12 m/s^2

g_p = 26.83 m/s²

g_p = 2683 cm/s² ( cm/s² = gal )