A body of density $d_{1}$ is counterpoised by $M g$ of weights of density $d_{2}$ in air of density $d$ . Then, the true mass of the body is

M

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\frac{M (1 - d / d_{2})}{(1 - d / d_{1})}

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M (1 - \frac{d}{d_{2}})

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M (1 - \frac{d}{d_{1}})

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Solution

The correct option is B $\frac{M (1 - d / d_{2})}{(1 - d / d_{1})}$
Let $M_{0} =$ mass of body in vacuum
Apparent weight of 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
$\Rightarrow M_{0} g - (\frac{M_{0}}{d_{1}}) d g = M g - (\frac{M_{0}}{d_{2}}) d g$
$\Rightarrow M_{0} = \frac{M (1 - \frac{d}{d_{2}})}{M (1 - \frac{d}{d_{1}})}$

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