JAMB - Physics (2004 - No. 30)
The earth is four times the size of the moon and the acceleration due to gravity on the earth is 80 times that on the moon. The ratio of the mass of the moon to that of the earth is
1:80
1:320
1:1280
1:4
Explication
NOTE: Firstly, it should be noted that the mass, as well as the weight of a body is independent of its size.
∴ Let the weight of the moon = Mm x gm
weight of the earth = Me x ge
But ge = 80gm
∴ weight of the earth = Me x 80gm
=> weight of the moon / weight of the earth = Mm x gm / Me x 80gm
thus Mm/Me ∝ gm/80gm ∝ 1/80
=> Mm:Me ∝ 1:80
∴ Let the weight of the moon = Mm x gm
weight of the earth = Me x ge
But ge = 80gm
∴ weight of the earth = Me x 80gm
=> weight of the moon / weight of the earth = Mm x gm / Me x 80gm
thus Mm/Me ∝ gm/80gm ∝ 1/80
=> Mm:Me ∝ 1:80