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1.Units, Dimensions and Measurement
easy
In a relation $F = a \,sin\, k_1x + b \,sin\, k_2t$ where $F , x$ and $T$ denote the force,distance and time respectively. Units of $k _{1}$ and $k _{2}$ are respectively
A$meter,s$
B$meter ^{-1}, s ^{-1}$
C$meter ^{-1}, s$
D$meter, s ^{-1}$
Solution
Using principle of dimensional homogeneity,
$| F |=\left|a \sin k_1 x\right|=\left|b \sin k_2 T \right|$
Since arguments can't have units, thus, $\left|k_1 x\right|=\left|k_2 T\right|=M^0 L^0 T^0$
Thus, $\left| k _1\right|= L ^{-1}$ and $\left| k _2\right|= T ^{-1}$
Thus units will be $k _1-$ metre $^{-1}$ and $k _2- s ^{-1}$.
$| F |=\left|a \sin k_1 x\right|=\left|b \sin k_2 T \right|$
Since arguments can't have units, thus, $\left|k_1 x\right|=\left|k_2 T\right|=M^0 L^0 T^0$
Thus, $\left| k _1\right|= L ^{-1}$ and $\left| k _2\right|= T ^{-1}$
Thus units will be $k _1-$ metre $^{-1}$ and $k _2- s ^{-1}$.
Standard 11
Physics
