If force F, acceleration A, and time T are taken as the fundamental physical quantities, the dimensions of length on this system of units are

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FAT²

FAT

AT²

answer is D.

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Detailed Solution

$L \propto F^{x} A^{y} T^{z} \Rightarrow [M^{0} L^{1} T^{0}] \propto {[M^{1} L^{1} T^{- 2}]}^{x} {[M^{0} L^{1} T^{- 2}]}^{y} {[M^{0} L^{0} T^{1}]}^{z} \Rightarrow [M^{0} L^{1} T^{0}] \propto [M^{x} L^{x + y} T^{- 2 x - 2 y + z}]$

$C o m p a r i n g p o w e r s, x = 0 x + y = 1 2 x - 2 y + z = 0$

$A f t e r S o l v i n g, x = 0, y = 1, z = 2 ∴ L \propto F^{0} A^{1} T^{2}$

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