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If momentum P, area A and time T are sel...

If momentum P, area A and time T are selected as fundamental quantities then energy has the dimensional formula

A

`[P^(2)A^(2)T^(-1)]`

B

`[P^(-1)A^(-1//2)T^(1)]`

C

`[P^(1)A^(1//2)T^(-1)]`

D

`[P^(-2)A^(-2)T^(1)]`

Text Solution

Verified by Experts

The correct Answer is:
C
`EpropP^(x)A^(y)T^(z)`
`E=k[M^(1)L^(1)T^(-1)]^(x)[L^(2)]^(y)[T^(1)]^(z)`
`[M^(1)L^(2)T^(-2)]=[M^(x)L^(x+2y)T^(x+z)]`
`x=1,y=(1)/(2),z=-1`
`E=kP^(1)A^(1//2)T^(-1)`
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Knowledge Check

  • If momentum (p), Area (A) and time (T) are takes as fundamental quantities, then energy has the dimensional formula :

    A
    `[pA^(1//2)T^(-1)]`
    B
    `[pA^(-1//2)T^(1)]`
    C
    `[p^(2)AT]`
    D
    `[pA^(-1)T]`

  • If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula

    A
    `[P^1 A^(-1) T^1]`
    B
    `[P^2 A^1 T^1]`
    C
    `[P^1 A^(-1//2) T^1]`
    D
    `[P^1 A^(1//2) T^(-1)]`

  • If momentum (p) , area (A) and time (t) are taken to be fundamental quantities then energy has the dimensional formula

    A
    `[p^(1)A^(-1)t^(-1)]`
    B
    `[p^(2)A^(1)t^(1)]`
    C
    `[p^(1)A^(1//2)t^(1)]`
    D
    `[p^(1)A^(1//2)t^(-1)]`

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