Question

Could somebody please look at the questions in the image and answer them for me? Please provide a detailed explanation with the answer. Thank you in advance!​

Answer 1

a) 3 N

b) 48 N

c) 24 N

d) 48 N

e) 6 N

Step-by-step 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