Question

Dimension of force of gravity is​

Answer 1

`M^(-1)L^(3)T^(-2)`

Step-by-step explanation:

Force has the unit N for Newton.

A Newton is
`m*(kg)/(s^(2) )` , mass*kilograms/seconds^2.

Dimensions in Physics include things such as Mass, Length, and Time.

kg is Mass

m is Length

s^2 is Time

So, since a Newton has all of these, it has T, L, and M. Force has dimensions
`T^(-2)LM`

However, you must now consider gravitational force.

Law of Gravitation states:

`F=(Gm_(1)m_(2)r )/(r^(2) )`

Convert that into a fraction with dimensions:

`F=(GM^(2) L)/(L^(2) )`

Remember force is
`T^(-2)LM`

Use the dimensions of force to find gravitational force, or G:

`F=(GM^(2) L)/(L^(2) )`

`T^(-2)LM=(GM^(2) L)/(L^(3) )`

`G=((T^(-2)LM)(L^(2)) )/(M*M)`

`G=((T^(-2)L^(3) M) )/(M^(2) )`

`G=M^(-1)L^(3)T^(-2)`