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Question

If the dimensions of length are expressed as a GxCyhz, where G, C and h are the universal gravitational constant, speed of light and plank constant respectively, then value of x,y,z will be :

A
x=1,y=32,z=12
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B
x=12,y=12,z=32
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C
x=12,y=32,z=12
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D
x=32,y=12,z=12
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Solution

The correct option is C x=12,y=32,z=12
Length GxCyhz
[L]=[M1L3T2]x[LT1]y[ML2T1]z
On comparing the power of M, L and T in both sides, we get
x+z=0 ....(i)
3x+y+2z=1 ....(ii)
and 2xyz=0 ....(iii)
By solving Eqs. (i), (ii) and (iii) we get
x=12;y=32 and z=12

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