First slide

Fluid statics

Question

A body of density d₁ is counterpoised by Mg of weights of density $d_{2}$ in air of density d. Then the true mass of the body is

Moderate

A

M
B

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

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

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

Solution

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
$\Rightarrow M_{o} g - (\frac{M_{o}}{d_{1}}) dg = Mg - (\frac{M}{d_{2}}) dg$
$\Rightarrow M_{o} = \frac{M [1 - \frac{d}{d_{2}}]}{[1 - \frac{d}{d_{1}}]}$

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