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  4. In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio 1: 3. The ratios of unit of length and time are, respectively,

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Q. In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio $1 : 3$. The ratios of unit of length and time are, respectively,

Physical World, Units and Measurements

Solution:

Length, $l=\frac{v^{2}}{a};$ time, $t=\frac{v}{a}$
$\Rightarrow $ Ratio of unit of length $=\left(\frac{1}{3}\right)^{2}=\frac{1}{9}$
$\Rightarrow $ Ratio of unit of time $=\frac{1}{3}$