Question

A body floats on water and then also on an oil of density 1.25. Which of the following is/are true? This question has multiple correct options
A. The body weighs less weight in oil than in water.
B. The volume of water displaced is 1.25 times that of oil displaced.
C. The body experiences equal up thrust from water and oil.
D. Apparent weight is zero in both cases.

Answer 1

Hint: In order to answer this question, we should be very sure about the floating conditions of a body in case of water and in case of oil. In both cases at first we have to assume the volume of the submerged body and that of the oil or water which is displaced by the submerged body respectively. Then we have to mention the floating conditions. On the basis of the following conditions we have to answer the various situations that are mentioned in the question.

Complete step by step answer:
We know that in water,
Let in this case the volume of the object submerged is equal to the volume of water displaced to be ${{v}_{1}}$.
So the floating conditions are:
$\begin{align}
  & \Rightarrow {{v}_{1}}g=vdg \\
 & \Rightarrow {{v}_{1}}=vd \\
\end{align}$
However, in case of oil we know that,
Let the volume of object submerged = volume of oil displaced = ${{v}_{2}}$
So the floating conditions are:
$\begin{align}
  & \Rightarrow {{v}_{2}}(1.25)g=vdg \\
 & \Rightarrow {{v}_{2}}=\dfrac{vd}{1.25}=\dfrac{{{v}_{1}}}{1.25} \\
 & \Rightarrow {{v}_{1}}=1.25{{v}_{2}} \\
\end{align}$
In both cases, the object is floating. So the apparent weight will be zero in both cases. Hence, the question has multiple answers.
The correct options are Options B, C, D.

Note: From the answer we already know that the apparent weight of a floating object is zero. This effect is quite different from that of the acceleration lift example. A floating or emerged body is not accelerating upwards or downwards so there can be no net force. In fact, buoyancy provides a supporting force which exactly acts as a ground.