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 GGG is the gravitational constant. In SI units, the units of force are kg⋅m/s^2, the units of mass are kg, and the units of distance are m. For this equation to have consistent units, the units of G must be which of the following?

a. kg3m⋅s^2
b. kg⋅s2m^3
c. m3kg⋅s^2
d. mkg⋅s^2

Answer 1

C. the units of G is m³/kg.s²

Step-by-step explanation:

Given;

magnitude of gravitational force,
`F = (Gm_1m_2)/(r^2)`

From the equation above, gravitational constant G is given as;

`F = (Gm_1m_2)/(r^2) \\\\G = (Fr^2)/(m_1m_2)\\\\G = (F)((1)/(m_1m_2))(r^2) \\\\G = ((kg.m)/(s^2))((1)/(kg^2) )(m^2)\\\\G = (m^3)/(kg.s^2)`

Thus, the correct option is "C" G = m³/kg.s²