Answer:
a) 3 N
b) 48 N
c) 24 N
d) 48 N
e) 6 N
Explanation:
Newton's law of gravitation states that the force between two masses is:
F = G m₁ m₂ / r²
At the original mass and distance, the force is 12 N.
12 = G m₁ m₂ / r²
a) If r is doubled:
F = G m₁ m₂ / (2r)²
F = G m₁ m₂ / (4r²)
F = 1/4 G m₁ m₂ / r²
F = 1/4 (12)
F = 3 N
b) If r is halved:
F = G m₁ m₂ / (r/2)²
F = G m₁ m₂ / (r²/4)
F = 4 G m₁ m₂ / r²
F = 4 (12)
F = 48 N
c) If one of the masses is doubled:
F = G (2 m₁) m₂ / r²
F = 2 G m₁ m₂ / r²
F = 2 (12)
F = 24 N
d) If both masses are doubled:
F = G (2 m₁) (2 m₂) / r²
F = 4 G m₁ m₂ / r²
F = 4 (12)
F = 48 N
e) If one of the masses is doubled and the distance is doubled:
F = G (2 m₁) m₂ / (2r)²
F = G (2 m₁) m₂ / (4r²)
F = 1/2 G m₁ m₂ / r²
F = 1/2 (12)
F = 6 N
