Question

The $S.I$. unit of length is "meter". Suppose we adopt a new unit of length which equals $x$ meter. Then, the area of $1\, m ^{2}$ expressed in terms of new unit has a magnitude__________

• A. $x$
• B. $x^{2}$
• C. $\frac{1}{x}$
• D. $\frac{1}{x^{2}}$

Answer 1

Answer: (D)

$SI$ unit of length $=$ metre $(m)$
New unit of length $=x$ metre
Hence, $1\, m=\frac{1}{x}$ new units
$\therefore $ Area, $1\, m^{2}=1\, m \times 1\, m$
$=\frac{1}{x} \times \frac{1}{x}=\frac{1}{x^{2}}$ (in new units)