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

Discussion Forum : Mechanical Properties Of Fluids

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 - \frac{d}{d_{2}} ⟯

C .

M ⟮ 1 - \frac{d}{d_{1}} ⟯

D .

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

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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