Question

The SI unit of force, the kilogram-meter per second squared (kg · m/s2), is called the newton (N). Find the dimensions and the SI units of the constant G in Newton's law of gravitation F = Gm1m2/r2. (For the dimension use L for length, M for mass, and T for time. For the units use m for meters, kg for kilograms, and s for seconds.)

Answer 1

SI unit of G,
`G=Nm^2/kg^2`

Step-by-step explanation:

The SI unit of force is Newton and it is denoted as N. The SI unit of length is meter or m. Similarly, the SI unit of mass is kilogram or kg.

The force acting between two masses is given by :

`F=G(m_1m_2)/(r^2)`

On rearranging,

`G=(Fr^2)/(m_1m_2)`

Putting all the units in above formula :

`G=(Nm^2)/(kg^2)`

So, the SI unit of G is :

`G=Nm^2/kg^2`