The masses of two planets are in the ratio of 1:7. The ratio between their diameters is 2: 1. The ratio of forces which they exert on each other is

CONCEPT:

Gravitational Force

• The gravitational force between two objects is given by Newton's law of gravitation:

  F = G * (m1 * m2) / r^2

• Where:
  • F is the gravitational force
  • G is the gravitational constant
  • m1 and m2 are the masses of the two objects
  • r is the distance between the centers of the two objects

EXPLANATION:

• Given:
  • The ratio of the masses of the two planets (m1/m2) = 1/7
  • The ratio of their diameters (d1/d2) = 2/1
• The distance between the centers of the two planets will be proportional to their diameters. Hence, the ratio of the distances (r1/r2) = 2/1.
• Using the formula for gravitational force:
  • F1 = G * (m1 * m2) / (r1)^2
  • F2 = G * (m1 * m2) / (r2)^2
• Since m1/m2 = 1/7 and r1/r2 = 2/1:
  • F1/F2 = (G * (m1 * m2) / (r1)^2) / (G * (m1 * m2) / (r2)^2)
  • = (r2)^2 / (r1)^2
  • = (1/2)^2
  • = 1/4
• Hence, the ratio of the forces which they exert on each other (F1/F2) is 1 : 1.

Therefore, the ratio of the forces which they exert on each other is 1 : 1.