Question

The ratio of masses of two planets is 2:3 and the ratio of their radii is 4:7. Find the ratio of their accelaration due to gravity.

Answer 1

Answer:

9:7

Explanation:

Acc to law of gravitation = g = GM/R²

Ratio of diameter and the radius -

R1 = 2/2 = 1

R2 = 3/2

g1/g2 = (GM1/R1²)/(GM2/R2²)

g1/g2 = M1/M2 × R2²/R1²

g1/g2 = 4/7 × ((3/2)/1)²

g1/g2 = 4/7 × (3/2)²

g1/g2 = 4/7 × 9/4

g1/g2 = 9/7

g1/g2 = 9/7

g1:g2 = 9:7

Thus,  the ratio of their acceleration due to gravity is 9:7

Answer 2

Answer:

According to law of gravitation (g) = GM/R²

Ratio of the diameter and the radius = R1=2/2=1

R2= 3/2

g¹/g²= (GM1/R1²)/(GM2/R2²)

g¹/g² = (4/7) × ((3/2)/1)²

g¹/g² = 4/7 × (3/2)²

g¹/g² = 4/7 × 9/4

g¹/g² = 9/7

g¹:g² = 9:7

Thus , the ratio of their accelerations due to gravity is 9:7.