The SI unit of length is 'metre'. Suppose we adopt a new unit of length which equals \(x\) metre. Then, the…
The SI unit of length is 'metre'. Suppose we adopt a new unit of length which equals \(x\) metre. Then, the area of \(1 \mathrm{~m}^2\) expressed in terms of new unit has a magnitude
\(x\)
\(x^2\)
\(\frac{1}{x}\)
\(\frac{1}{x^2}\)
Solution
SI unit of length = metre (m)
New unit of length \(=x\) metre
Hence, \(\quad 1 \mathrm{~m}=\frac{1}{x}\) new units
\(\therefore \quad\) Area, \(1 \mathrm{~m}^2=1 \mathrm{~m} \times 1 \mathrm{~m}\)
\(=\frac{1}{x} \times \frac{1}{x}=\frac{1}{x^2} \text { (in new units) }\)