Physics - Gravitation

9 First, consider the case of Earth. by the conservation of energy.

(K_i + U_i) = (K_f + U_f)

Sub. K_i = (1/2)mV_0 ; U_i = -GMm/R and K_f = U_f = 0

We have (1/2)mV_0 = GMm/R

where m: the mass of the object, M: the mass of the Earth. R: the radius of the Earth.

V_0 = √(2GM/R)

Now, for the palent, R' = 3R and ρ' = 2ρ => M' = 54M

V = √(108GM/3R) = √18√(2GM/R) = 3√2 V_0 => (D)