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A force F is given by F = at + bt^(2) , ...

A force `F` is given by `F = at + bt^(2)` , where `t` is time . What are the dimensions of `a and b`?

Text Solution

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From the principle of dimensional homogenity , `[ F] = [ at]`
:. ` [ a] = [(F)/(t) ] = [ (MLT^(-2))/( T)] = [ MLT^(-3)`
Similarly ,`[F] = [ bt^(2)]`
:. `[b] = [(F)/(t^(2))] = [ (MLT^(-2))/( T^(2))] = [ MLT^(-4)]`
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