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Which of the following product of e,h,mu...

Which of the following product of `e,h,mu,` `G` (where `mu` is the permeability ) be taken so that the dimensions of the product are same as that of speed of light ?

A

`he^(-2)mu^(-1)G^(0)`

B

`h^(2)eG^(0)mu`

C

`h^(0)e^(2)G^(-1)mu`

D

`hGe^(-2)mu^(0).`

Text Solution

Verified by Experts

The correct Answer is:
A
Here `v=e^(a)h^(b)mu^(c )G^(d).` Taking the dimensions `M^(0)LT^(-1)A^(0)=[AT^(1)]^(a)[ML^(2)T^(-1)]^(b)[MLT^(-2)A^(-2)]^(c )[M^(-1)L^(3)T^(-2)]^(d).` There will be `4` simultaneous equations by equating the dimensions of `M,L,T` nad `A`. They are
`a-2c=0`
`a-b-2c-2d=-1`
`b+c-d=0`
`2b+c+3d=1`
Solving for `.a., .b., .c.` and `.d.` we get `a=-2,b=1,`
`c=-1,d=0.` Thus `v=e^(-2)hmu^(-1)G^(0).`
Hence correct choice is `(a)`.
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