If $$R=\left\{\left(x,y\right):y=2x\right\}$$ is a relation in $$A=\left\{1,2,3,4,6,7,8\right\}$$ then write all the elements of $$R$$

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Subjective Type
Find the value of $$60\,J$$ per min on a system that has $$100\,g, 100\,cm$$ and $$1$$ min as the base unit.
Solution
We have to find the value of $$60\,J/min,$$ if $$100\,g, 100\,cm$$ and $$1\,min$$ as base unit.
Dimensions of power = $$ML^{2} T^{-3}$$
e.g., S.I unit of Power = $$1 \,Kg.m^{2} / s^{3}$$
$$= (1\,kg / 100\,g) \cdot (1\,m / 100\,cm)^{2} / (1\,sec / 1\,min)^{3}$$
$$= (10) \times 1 \times (60)^{3}$$
$$= 2160000 = 2.16 \times 10^{6}$$ unit
Now, $$60\,J/min = 60\,kg/m^{2} / s^{2}min = 1\,Kg.m^{2}/s^{3}$$
But $$1\,kg.m^{2} / s^{3} = 2.16 \times 10^{6}$$ unit
so, value of $$60\,J/min = 2160000$$ or $$2.16 \times 10^{6}$$ unit
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