A body of density d1 is counterpoised by Mg of weights of density d2 in air of d

Question

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

Options:

A . M

B . M⟮1−dd2⟯

C . M⟮1−dd1⟯

D . M(1−dd2)(1−dd1)

Answer: Option D
:
D
Let

M_{O}

=mass of body in vacuum.
Apparent weight of the body in air = Apparent weight of standard weights in air
Actual weight of the body - upthrust due to displaced air
= Actual weight of the weights- 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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