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

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Solution

The correct option is 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 $\Rightarrow M_{0} g - (\frac{M_{0}}{d_{1}}) d g == M g - (\frac{M}{d_{2}}) d g \Rightarrow M_{0} = \frac{M [1 - \frac{d}{d_{2}}]}{[1 - \frac{d}{d_{1}}]}$

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A body of density d1 is counterpoised by M g of weights of density d2 in air of density d. Then the true mass of the body is

The correct option is D Let M_0 mass of body in vacuum. Apparent weight of the body in air = Apparent weight of standard weights in air ⇒Actual weight – upthrust due to displaced air = Actual weight – upthrust due to displaced air ⇒M0g−(M0d1)dg==Mg−(Md2)dg⇒M0=M[1−dd2][1−dd1]

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