Question

Calculate the value of Acceleration due to gravity on the surface of the planet ( given - mass of planet = 7.4×10²² kg, radius of planet = 4958km ,
G= 6.7 ×10-¹¹

Answer 1

Given data :

➜ Mass of planet, M = 7.4 * 10²² kg

➜ Radius of planet, R = 4958 km

➜ Gravitational constant, G = 6.7 * 1/10¹¹ N m²/kg²

Solution : To calculate the value of acceleration due to gravity on the surface of the planet, we use formula of acceleration due to gravity;

➜ Acceleration due to gravity, g = [GM]/[R]²

Now here,

➜ g = [GM]/[R]²

By substituting the values:

➜ g = [(6.7 * 1/10¹¹) * (7.4 * 10²²)]/[4958]²

➜ g = [(6.7 * 7.4) * (10²²/10¹¹)]/[24581764]

➜ g = [49.58 * 10¹¹]/[24581764]

➜ g = [49.58/24581764] * 10¹¹

➜ g = [1/495800] * 10¹¹

➜ g = 10¹¹/495800

➜ g = 10⁹/4958

➜ g = (1/4958) * 10⁹

➜ g = 0.00020169423 * 10⁹

➜ g = 201694.23 m/s²

Answer : Hence, the value of acceleration due to gravity on the surface of the planet is 201694.23 m/s².