Question

A body floats in a liquid contained in a beaker. The whole system falls freely under gravity. The upthrust on the body is -

• A. Zero
• B. Equal to the weight of the liquid displaced
• C. Equal to the weight of the body in air.
• D. Equal to the weight of the immerssed portion of the body

Answer 1

The correct option is A Zero

We know that
$F_{\text{upthrust}}=V\rho g_{eff}----\left(1\right)$
where $V$ is volume of body and $\rho$ is the density of liquid.
$g_{eff}=|\overrightarrow{g}-\overrightarrow{a}|$
As whole system falls freely under gravity, therefore $\overrightarrow{a}=-g$.
Hence, $g_{eff}=-g-(-g)=0$
$\therefore F_{upthrust}=0$ [from (1)]