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  4. If force F is related with distance x and time t as F=A√x+Bt2 , the dimensions of (A/B) is

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Q. If force $F$ is related with distance $x$ and time $t$ as $F=A\sqrt{x}+Bt^{2}$ , the dimensions of $\frac{A}{B}$ is

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

All terms of an equation must have same dimensions
$\left[M L T^{- 2}\right]=\left[A L \frac{1}{2} \, \right]=\left[B T^{2}\right]$

$\left[A\right]=\frac{M L T^{- 2}}{\sqrt{L}}$
$\left[B\right]=\frac{M L T^{- 2}}{T^{2}}$