First slide

Dimensions of physical quantities

Question

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

Easy

A

FAT²
B

FAT
C

FT
D

AT²

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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