What are the dimensions of Planck’s constant and gravitational constant?

Solution

Energy of a photon is given by, E = hv
where 'h' is the planck's constant.

space space therefore

space space space space space space space space space space space space straight h space equals space straight E over straight v equals fraction numerator open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 2 end exponent close square brackets over denominator straight M to the power of 0 straight L to the power of 0 straight T to the power of 1 end fraction equals open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 1 end exponent close square brackets

Gravitational constant,
We know,

italic space italic space F italic equals G fraction numerator M m over denominator r to the power of italic 2 end fraction

space space space space space therefore

space space space space space space space space space space space space space straight G space equals space Fr squared over Mm equals fraction numerator open square brackets straight M to the power of 1 straight L to the power of 1 straight T to the power of negative 2 end exponent close square brackets open square brackets straight L squared close square brackets over denominator open square brackets straight M to the power of 1 close square brackets open square brackets straight M to the power of 1 close square brackets end fraction

space space space space equals space open square brackets straight M to the power of negative 1 end exponent straight L cubed straight T to the power of negative 2 end exponent close square brackets

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