Question

A planet has a mass of 6.14 x 1023 kg and a radius of 2.85 x 106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 58.4-kg person weigh on this planet?

Answer 1

ANSWERS

(a) 5.04 m/s²

(b) 294.34 N

Step-by-step explanation

Given:

• The mass of the planet, M = 6.14 x 10²³ kg

,

• The radius of the planet, R = 2.85 x 10⁶ m

,

• The mass of a person standing on this planet, m = 58.4 kg

(a) The acceleration due to gravity in a planet of mass M and radius R is,

`g=(G\cdot M)/(R^2)`

Where G is the gravitational constant with a value of 6.67 x 10⁻¹¹ Nm²/kg².

Replacing the known values and solving we get the acceleration due to gravity of this planet,

`g=(6.67\cdot10^(-11)Nm^2/kg^2\cdot6.14\cdot10^(23)kg)/((2.85\cdot10^6)^2m^2)\approx5.04m/s^2`

Hence, the acceleration due to gravity is 5.04 m/s², rounded to two decimal places.

(b) The weight of an object of mass m is the product of its mass and the acceleration due to gravity,

`weight=m\cdot g=58.4kg\cdot5.04m/s^2\approx294.34N`

Hence, a 58.4-kg person would weigh 294.34 N on this planet, rounded to two decimal places.