Express mass in terms of dimensions of velocity of light,Planck's constant and gravitational constant

Question

Khimraj · Answer

Here, [ c ] = L T − 1 [ G ] = M − 1 L 3 T − 2 [ h ] = M 1 L 2 T − 1 Let m = c x G y h z By substituting the dimensions of each quantity in both the sides, M = ( L T − 1 ) x ( M − 1 L 3 T − 2 ) y ( M L 2 T − 1 ) z M = [ M y + z L x + 3 y + 2 z T x − 2 y − z ] By equating the power of M, L, T in both the sides: − y + z = 1 , x + 3 y + 2 z = 0 , − x − 2 y − z = 0 By soling the above equation , We get, x = 1 2 , y = − 1 2 , and z = 1 2 So, [ m ] = c 1 2 G − 1 2 h 1 2

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Express mass in terms of dimensions of velocity of light,Planck's constant and gravitational constant

Express mass in terms of dimensions of velocity of light,Planck's constant and gravitational constant

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