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Dimensional Analysis

In a relation...

Question

In a relation $F = a s i n k_{1} x + b s i n k_{2} T$ where $F, x$ and $T$ denote the force, distance and time respectively. Units of $k_{1}$ and $k_{2}$ are respectively a

m e t e r, s

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m e t e r^{- 1}, s^{- 1}

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m e t e r^{- 1}, s

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m e t e r, s^{- 1}

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Solution

The correct option is B $m e t e r^{- 1}, s^{- 1}$
Using principle of dimensional homogeneity,
$| F | = | a s i n k_{1} x | = | b s i n k_{2} T |$
Since arguments can't have units, thus, $| k_{1} x | = | k_{2} T | = M^{0} L^{0} T^{0}$
Thus, $| k_{1} | = L^{- 1}$ and $| k_{2} | = T^{- 1}$
Thus units will be $k_{1}$ -- $m e t r e^{- 1}$ and $k_{2}$ -- $s^{- 1}$ .

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