Question

If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ‘g’ on the earth is 9.8 ms^–2, then the value of ‘g’ on that planet is = ……... ms^–2 

(A) 4.9 

(B) 0.98 

(C) 0.49 

(D) 49

Answer 1

Correct option: (C) 0.49

Explanation:

Let m₁, R₁, g be mass, radius and acceleration for earth. m₂, R₂, g' be mass, radius and acceleration for planet

m₁ = 80m₂ 

R₁ = 2 R₂ 

g = 9.8

g = (GM / R²)

(g' / g) = (M₂ / R₂²) × (R₁² / M₁)

= (M₂ / M₁) × (R₁ / R₂)² 

= (1 / 80) × (2)² 

(g' / g) = (1 / 20)

g' = (g / 20)

g' = (9.8 / 20)

= 0.49 m/s²