A physical quantity x depends on quantities y and z as follows: x=Ay+Btan(Cz), where A, B and C are constants. Which of the following do not have the same dimensions?
A
x and B
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B
C and z−1
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C
y and B/A
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D
x and A
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Solution
The correct option is Dx and A From the given equation, using principle of homogeneity: [x]=[A][y]=[B]
and [C][z]=1
So, we can say that [x]=[B], [C]=[z−1] and [y]=[B][A].