First slide

Dimensions of physical quantities

Question

If force F, length L and time T be considered fundamental units of mass will be

Moderate

A

$[F L T^{- 2}]$
B

$[F L^{- 2} T^{- 1}]$
C

$[F L^{- 1} T^{2}]$
D

$[F^{2} L T^{- 2}]$

Solution

Let $[M] \propto [F^{a} L^{b} T^{c}]$
So, using dimensions, we have
$[M^{1} L^{0} T^{0}] = K {[M L T^{- 2}]}^{a} {[L]}^{b} {[T]}^{c}$
$= K [M^{a} L^{a + b} T^{- 2 a + b}]$
We have, a =1, a = b = 0 and k =1
$∴ b = - 1$
and $- 2 a + c = 0$
$\Rightarrow c = 2$
So unit of mass is $[F L^{- 1} T^{2}]$

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