Physics

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

${ FM }^{ -1 }{ T }^{ 2 }$

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

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Single Correct Medium Published on 18th 08, 2020
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