Physics

Find the dimensions of G in the equation $$F=\dfrac{Gm_{1}m_{2}}{r^{2}}$$ ; where F is the force of gravitational attraction between two bodies of point masses $$ m_{1}$$ and $$m_{2}$$ , 'r' is the distance of separation between them.


SOLUTION
The gravitational force acting between the two bodies is given by:
$$F=G\dfrac{m_1m_2}{r^2}$$

$$G=\dfrac { F{ r }^{ 2 } }{ { m }_{ 1 }{ m }_{ 2 } } $$

The dimension of the force is $$[MLT^{-2}]$$

$$ =\dfrac { \left[ ML{ T }^{ -2 } \right] \left[ { L }^{ 2 } \right]  }{ \left[ M \right] \left[ M \right]  } ={ M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 }$$
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Subjective Medium Published on 18th 08, 2020
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