Question

If you can jump 0.5 m in the air on earth, how high can you jump on a planet whose mass is half of earth’s mass? (You can assume the density is the same) Options:- 1) 7.8 m 2) 3.4 m 3) 0.5 m 4) 0.62 m

Answer 1

Answer:

The surface gravity (g) of a body depends on the mass (M) and the radius (r) of the given body. The formula which relates these quantities is:

g = G * M / r^2.

G = 6.67 * 10^-11 Newton-meter^2/kilogram^2

which is a constant.

Since the radius of the planet is halved the mass will be one eighth that of Earth (volume being a cube function and (1/2) ^ 3 = 1/8)

The radius squared would be one fourth (1/2)^2 = 1/4.

Therefore g1 = G * 1/8 M / 1/4r.

1/8 divided by 1/4 is 1/2 so the surface gravity of the smaller planet would be 1/2 or 50% of Earth.

Given the same muscular strength a person should be able to jump twice as high or 2.6 m.