Q143 / 160 · WBJEE 2011 · Physics

An object weighs \(\mathrm{m}_1\) in a liquid of density \(\mathrm{d}_1\) and that in liquid of density \(\mathrm{d}_2\) is \(\mathrm{m}_2\). The density \(d\) of the object is

  • A
    \(\mathrm{d}=\frac{\mathrm{m}_2 \mathrm{~d}_2-\mathrm{m}_1 \mathrm{~d}_1}{\mathrm{~m}_2-\mathrm{m}_1}\)
  • B
    \(d=\frac{\mathrm{m}_1 \mathrm{~d}_1-\mathrm{m}_2 \mathrm{~d}_2}{\mathrm{~m}_2-\mathrm{m}_1}\)
  • C
    \(\mathrm{d}=\frac{\mathrm{m}_2 \mathrm{~d}_1-\mathrm{m}_1 \mathrm{~d}_2}{\mathrm{~m}_1-\mathrm{m}_2}\)
  • Correct answer
    D
    \(\mathrm{d}=\frac{\mathrm{m}_1 \mathrm{~d}_2-\mathrm{m}_2 \mathrm{~d}_1}{\mathrm{~m}_1-\mathrm{m}_2}\)

Solution

Hints: \(V\left(d-d_1\right) g=m_1 g\) \(\mathrm{V}\left(\mathrm{d}-\mathrm{d}_2\right) \mathrm{g}=\mathrm{m}_2 \mathrm{~g}\) \(\frac{\mathrm{d}-\mathrm{d}_1}{\mathrm{~d}-\mathrm{d}_2}=\frac{\mathrm{m}_1}{\mathrm{~m}_2} \quad \therefore \mathrm{d}=\frac{\mathrm{m}_1 \mathrm{~d}_2-\mathrm{m}_2 \mathrm{~d}_1}{\mathrm{~m}_1-\mathrm{m}_2}\)

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

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