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What is the dimensional formula of (1)/(...

What is the dimensional formula of `(1)/(mu_(0)epsilon_(0))` where the symbols have their usual meanings?

A

`[M^(0)L^(2)T^(2)]`

B

`[M^(0)L^(2)T^(-2)]`

C

`[M^(0)L^(-1)T^(2)]`

D

`[M^(0)L^(1)T^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:
b
The velocity of light `C=(1)/(sqrt(mu_(0)epsilon_(0))) therefore C^(2)=(1)/(mu_(0)epsilon_(0))`
`therefore` The dimensions of `(1)/(mu_(0)epsilon_(0))` are the same as that of `C^(2)`. `[C^(2)]=[(L)/(T)]^(2)=[M^(0)L^(2)T^(-2)]`
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Knowledge Check

  • The dimensional formula of sqrt((mu_(0))/(epsilon_(0))) is

    A
    `[ ML^(2) T^(-3) A^(2)]`
    B
    `[M^(0) LT^(-1) A^(0)]`
    C
    `[ ML^(2) T^(-3) A^(-2)]`
    D
    `[ M^(-1) L^(-2) T^(3) A^(2) ]`

  • Dimension of (1)/(mu_(0)epsilon_(0)) , where symbols have usual meaning, are

    A
    (a) `[L^(-1)T]`
    B
    (b) `[L^(-2)T^(2)]`
    C
    ( c ) `[L^(2)T^(-2)]`
    D
    (d) `[LT^(-1)]`

  • The dimensional formula mu_(0)epsilon_0 is

    A
    `M^0L^(-2)T^2`
    B
    `M^0 L^2T^(-2)`
    C
    `M^(0) L^(1) T^(-1)`
    D
    `M^(0) L^(-1) T^(1)`

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