Question

An object on a planet has a mass of 243 kg. What is the acceleration of the object, if the radius of the planet is 2.32 x 10^7 m , and the mass of planet is 6035 x 10^30 kg? Estimate G as 6067 x 10^-11 N (m/kg)^2

Answer 1

The acceleration of the object is 7.87 x 10⁵ m/s²

Step-by-step explanation:

Given;

mass of the object, m = 243 kg

mass of the planet, M = 6.35 x 10³⁰ kg

radius of the planet, R = 2.32 x 10⁷ m

universal gravitation constant, G = 6.67 x 10⁻¹¹ Nm/kg²

Apply Newton's second law of motion and Newton's gravitational law;

`ma = (GmM)/(R^2)\\\\a = (GM)/(R^2)\\\\a = ((6.67*10^(-11))(6.35*10^(30)))/((2.32*10^7)^2)\\\\a = (4.2355*10^(20))/(5.3824*10^(14)) \\\\a = 786916.2 \ m/s^2\\\\a = 7.87*10^5 \ m/s^2`

Therefore, the acceleration of the object is 7.87 x 10⁵ m/s²