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 equationF=Gm1m2r2where F is the magnitude of the gravitational attraction on either body, m1 and m2 are the masses of the bodies, r is the distance between them, and G is the gravitational constant. In SI units, the units of force are kgâ‹…m/s2, 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?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,where is the magnitude of the gravitational attraction on either body, and are the masses of the bodies, is the distance between them, and is the gravitational constant. In SI units, the units of force are , the units of mass are , and the units of distance are . For this equation to have consistent units, the units of must be which of the following?A. kg3mâ‹…s2B. kgâ‹…s2m3C. m3kgâ‹…s2D. mkgâ‹…s2

Answer 1

The S.I unit of G must be m³/kg.s² to keep the equation consistent.

Step-by-step explanation:

We have the equation:

F = Gm₁m₂/r²

where,

F = Gravitational Force between Two Bodies

G = Gravitational Constant

m₁ = Mass of 1st Body

m₂ = Mass of 2nd body

r = Distance between the Bodies

The S.I Units of the quantities are:

F = Newton = kg.m/s²

m₁ = kg

m₂ = kg

r = meter = m

G = ?

Therefore, to find the units of Gravitational Constant (G), we substitute the known units in the formula:

kg.m/s² = G(kg)(kg)/m²

G = m³/kg.s²