Question

the acceleration due to gravity on the surface of a planet is 3.5 times larger a site is on the surface of earth. the mass density of the planert is known to be 1.5 itmes that of earth. wha t is the radius of this planet in terms of earth's radius g

Answer 1

The radius of this planet in terms of earth's radius is 0.65 times Earth's radius.

How to calculate the radius of the planet?

The radius of the Planet is calculated by applying the following formula as shown below;

g = GM/R²

where;

• M is mass
• R is radius
• g is acceleration due to gravity
• G is universal gravitation constant

G = gR² / M

mass = density x volume

M = ρV

G = gR² / M

G = gR² / ρV

R² = GρV/g

R = √(GρV/G)

For the planet;

G = (3.5 x g x r² )/ (1.5 x ρV)

G = 2.33gr²/ρV

r² = GρV/2.33g

r² = 0.428 GρV / g

r = √0.428 GρV / g

r = 0.65√(GρV/G)

r = 0.65R