Physics

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


ANSWER

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


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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