Question

An object of weight $W$ and density $\rho$ is submerged in a fluid of density ${\rho }_1$. Its apparent weight will be

• A. $W(\rho -{\rho }_1)$
• B. $\frac{(\rho -{\rho }_1)}{W}$
• C. $W(1-\frac{{\rho }_1}{\rho })$
• D. $W({\rho }_1-\rho )$

Answer 1

Answer: (C)

$W(1-\frac{{\rho }_1}{\rho })$

Weight of object in vacuum = W ; It's density = $\rho$

Therefore, the volume of the object will be V = $W/\rho$

Now, this object is immersed in a fluid of density ${\rho }_1$

Its apparent loss in weight would be equal to the weight of fluid displaced (as is evident from Archimedes' principle)

Apparent loss = ${\rho }_{1}V$ = ${\rho }_{1}W/\rho$

Therefore, the weight in water = weight in vacuum - the loss in weight

Weight in water = $W-{\rho }_{1}W/\rho$

= $W(1-{\rho }_1/\rho )$