A body of density ${d_1}$ is counterpoised by $Mg$ of weights of density ${d_2}$ in air of density $d$. Then the true mass of the body is
A$M$
B$M\,\left( {1 - \frac{d}{{{d_2}}}} \right)$
C$M\left( {1 - \frac{d}{{{d_1}}}} \right)$
D$\frac{{M(1 - d/{d_2})}}{{(1 - d/{d_1})}}$
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D$\frac{{M(1 - d/{d_2})}}{{(1 - d/{d_1})}}$
d (d)Let ${M_0} = $mass of body in vacuum.
Apparent weight of the body in air = Apparent weight of standard weights in air
$ \Rightarrow $ Actual weight -upthrust due to displaced air
= Actual weight -upthrust due to displaced air
$ \Rightarrow $${M_0}g - \left( {\frac{{{M_0}}}{{{d_1}}}} \right)\,dg = Mg - \left( {\frac{M}{{{d_2}}}} \right)\,dg$$ \Rightarrow {M_0} = \frac{{M\left[ {1 - \frac{d}{{{d_2}}}} \right]}}{{\left[ {1 - \frac{d}{{{d_1}}}} \right]}}$
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