Q121 / 160 · AP EAMCET 2020 (21 Sep Shift 1) · Physics

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

  • A
    \(x\)
  • B
    \(x^2\)
  • C
    \(\frac{1}{x}\)
  • Correct answer
    D
    \(\frac{1}{x^2}\)

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, \(1 \mathrm{~m}^2=1 \mathrm{~m} \times 1 \mathrm{~m}\) \(=\frac{1}{x} \times \frac{1}{x}=\frac{1}{x^2} \text { (in new units) }\)

Hence, the correct answer is option: 'D'.

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