Question

Dimension of force of gravity is​

Answer 1

Answer:

$M^{-1}L^{3}T^{-2}$

Explanation:

Force has the unit N for Newton.

A Newton is $m*\frac{kg}{s^{2} }$ , 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:

$F=\frac{Gm_{1}m_{2}r }{r^{2} }$

Convert that into a fraction with dimensions:

$F=\frac{GM^{2} L}{L^{2} }$

Remember force is  $T^{-2}LM$

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

$F=\frac{GM^{2} L}{L^{2} }$

$T^{-2}LM=\frac{GM^{2} L}{L^{3} }$

$G=\frac{(T^{-2}LM)(L^{2}) }{M*M}$

$G=\frac{(T^{-2}L^{3} M) }{M^{2} }$

$G=M^{-1}L^{3}T^{-2}$