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Question

The speed of light c, gravitational constant G and planck’s constant h are taken as fundamental units in a system. The dimensions of time in this new system should be

A
[G12h12c52]
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B
[G52h12c12]
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C
[G12h12c32]
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D
[G12h12c52]
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Solution

The correct option is A [G12h12c52]
Here, [c] = LT1
[G]=M1L3T2
[h]=M1L2T1
Let, tcxGyhz
By substituting the dimensions of each quantity in both the sides,
T=(LT1)x(M1L3T2)y(ML2T1)z
By equating the power of M, L, T in both the sides,
y+z=0
x+3y+2z=0
x2yz=1
By solving the above equation,
We get, x=52,y=12,z=12
So, [t]=[c52G12h12]

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