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Question: If force, acceleration and time are taken as fundamental quantities, then the dimensions of length w...

If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be –

A

FT2\text{F}\text{T}^{2}

B

F-1A2T-1F^{\text{-1}}A^{2}T^{\text{-1}}

C

FA2T\text{F}\text{A}^{2}T

D

AT2\text{A}\text{T}^{2}

Answer

AT2\text{A}\text{T}^{2}

Explanation

Solution

[AT2] = [A] [T]2 = LT-2 T2 = L\mathbf{\lbrack}\text{A}\text{T}^{\mathbf{2}}\mathbf{\rbrack}\mathbf{\ }\mathbf{=}\mathbf{\ }\mathbf{\lbrack}\mathbf{A}\mathbf{\rbrack}\mathbf{\ }\mathbf{\lbrack}\mathbf{T}\mathbf{\rbrack}^{\mathbf{2}}\text{ }\mathbf{=}\text{ L}\text{T}^{\text{-2}}\text{ }\text{T}^{\mathbf{2}}\mathbf{\ }\mathbf{=}\text{ L}