Physics

# If force $F$, length $L$ and time $T$ are chosen as fundamental quantities, then the dimensional formula for mass is:

${ F }^{ 1 }{ L }^{ -1 }{ T }^{ 2 }$

##### SOLUTION
Mass $=M^{1}L^{0}T^{0}=F^{\alpha}L^{\beta}T^{\gamma}$
$M^{1}L^{0}T^{0}=(MLT^{2})^{\alpha}(L)^{\beta}(T)^{\gamma}$
$M^{1}L^{0}T^{0}=M^{\alpha}L^{\alpha+\beta}T^{-2\alpha+\gamma}$
$\alpha=1,\alpha+\beta=0 \Rightarrow \beta=-1$
$-2 \alpha + \gamma=0$
$\Rightarrow \gamma =2$
$\Rightarrow Mass = F^{1}L^{-1}T^{2}$

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Single Correct Medium Published on 18th 08, 2020
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