Question

Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The force of gravitational attraction is represented by the equation F=Gm1m2r2, where F is the magnitude of the gravitational attraction on either body, m1 and m2 are the masses of the bodies, rrr is the distance between them, and G is the gravitational constant. In SI units, the units of force are kg⋅m/s2, the units of mass are kg, and the units of distance are mm. For this equation to have consistent units, the units of G must be which of the following?

A. kg3m⋅s2
B. kg⋅s2m3
C. m3kg⋅s2
D. mkg⋅s2

Answer 1

C m³/kgs²

Step-by-step explanation:

From the question, we know that

F = Gm1m2/R², where

F = the Force of gravity in N.

G = gravitational constant, in Nm²/kg²

m1 = mass in kg

m2 = mass in kg

R = distance between the objects in m

Now, if we substitute the units of each in the formula, we have

N = G * (kg * kg) / m²

N = G (kg²) / m²

Nm² = G kg², remember, N itself is kgm/s², so we substitute for that

Kgm/s² * m² = G kg²

Kgm³/s² = G kg²

G = (kgm³/s²) / kg²

G = m³/kgs²

And that's our answer