If C is the velocity of light,h is Planck's c | vedclass

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(B) Let the mass $M$ be expressed as $M = C^a h^b G^c$.The dimensions are:$C = [LT^{-1}]$$h = [ML^2T^{-1}]$$G = [M^{-1}L^3T^{-2}]$Substituting these i

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$h^{1/2} C^{1/2} G^{-1/2}$

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(B) Let the mass $M$ be expressed as $M = C^a h^b G^c$.The dimensions are:$C = [LT^{-1}]$$h = [ML^2T^{-1}]$$G = [M^{-1}L^3T^{-2}]$Substituting these into the equation:$[M^1L^0T^0] = [LT^{-1}]^a [ML^2T^{-1}]^b [M^{-1}L^3T^{-2}]^c$$[M^1L^0T^0] = M^{b-c} L^{a+2b+3c} T^{-a-b-2c}$Comparing the powers of $M, L, T$ on both sides:$b - c = 1$ $(i)$$a + 2b + 3c = 0$ (ii)$-a - b - 2c = 0$ (iii)Adding (ii) and (iii): $b + c = 0$,so $b = -c$.Substituting $b = -c$ into $(i)$: $-c - c = 1 \implies -2c = 1 \implies c = -1/2$.Then $b = 1/2$.Substituting $b = 1/2$ and $c = -1/2$ into (iii): $-a - 1/2 - 2(-1/2) = 0 \implies -a - 1/2 + 1 = 0 \implies a = 1/2$.Thus,$M = C^{1/2} h^{1/2} G^{-1/2}$.

If $C$ is the velocity of light,$h$ is Planck's constant,and $G$ is the gravitational constant,and these are taken as fundamental quantities,then the dimensional formula of mass is:

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