Question

The acceleration due to gravity on the surface of a planet is five times as large as it is on the surface of Earth. The mass density of the planet is known to be four times that of Earth. What is the radius of this planet in terms of Earth's radius?

Answer 1

Answer:

1.25 R

Explanation:

Acceleration due to gravity on earth, ge = g

Acceleration due to gravity on planet, gP = 5 times the acceleration due to gravity on earth

gP = 5 g

Density of planet = 5 x density of earth

Let the radius of earth is R

Let the radius of planet is Rp.

Use the for acceleration due to gravity

$g = \frac{4}{3}G\pi R\rho$

where, G s the universal gravitational constant and ρ be the density of planet.

For earth

$g = \frac{4}{3}G\pi R\rho$ .... (1)

For planet

$g_{P} = \frac{4}{3}G\pi R_{P}\rho_{P}$

According to the question

gp = 5 g, ρP = 4 ρ

Substitute the values

$5g = \frac{4}{3}G\pi R_{P}\4rho$   .... (2)

Divide equation (2) by equation (1), we get

$5=\frac{R_{p\times 4\rho }}{R\rho }$

Rp = 1.25 R

Thus, the radius of planet 1.25 R.