Question

In physics, every physical quantity is measured with respect to a unit. Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. Knowing the units of physical quantities will help you solve problems in physics.

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= Gm1m2 /r^2

where 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 Sl 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. kg^3/ms^2
b. kgs^2/m^3
c. m^3/kgs^2
d. m/kgs^2

Answer 1

Answer:

Unit of G = m³/kg s²

Explanation:

The force of gravitational attraction is represented by the equation.

$F=G\dfrac{m_1m_2}{r^2}$

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. G is the gravitational constant.

We need to find the unit of G.

Rearranging the above formula for G.

$G=\dfrac{Fr^2}{m_1m_2}$

Putting units of F,m and r such that,

$G=\dfrac{N\times m^2}{kg^2}\\\\\because N=kgm/s^2\\\\G=\dfrac{kg\times m\times m^2}{kg^2\times s^2}\\\\G=m^3/kgs^2$

Hence, the correct option is (c) m³/kg s².