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Write the dimensions of a//b in the rela...

Write the dimensions of `a//b` in the relation `F = a sqrtx + bt^2` where F is force x is distance and t is time.

Text Solution

Verified by Experts

The correct Answer is:
`[L^(-1//2) T^2]`
`asqrtx` has the dimensions of force F
`:. a = F|sqrtx = MLT^(-2) / L^(1//2) = M^1 L^(1//2) T^(-2)`
Similarly,
`b = F|t^2 = MLT^(-2)|T^2 = M^1L^1T^(-4)`
`:. (a)/(b) = (ML^(1//2)T^(-2))/(MLT^(-4)) = [L^(-1//2T^2)]`
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Knowledge Check

  • The dimensions of (a)/(b) in the relatin F = ax + bt are

    A
    `LT^(-1)`
    B
    `L^(-1)T`
    C
    LT
    D
    `L^(-1)T^(-1)`

  • The dimensions of a/b in the equation P=(a-t^(2))/(bx) where P is pressure, x is distance and t is time are

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

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