Question

A rock weighs $1400N$ in air and has an apparent weight of $900N$ when submerged in fresh water $\left(998kg/m^3\right)$. The volume $\left(in{m}^3\right)$ of the rock is $(g=9.8m/s^2)$.

• A. $1.4\times {10}^2$
• B. $6\times {10}^{-2}$
• C. $9\times {10}^{-2}$
• D. $5.1\times {10}^{-2}$

Answer 1

The correct option is D $5.1\times {10}^{-2}$

Answer is D.

Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object.
Buoyancy force can be calculated with the equation $Fb=Vs\times D\times g$, where $F_b$ is the buoyancy force, $V_s$ is the submerged volume, $D$ is the density of the fluid the object is submerged in, and $g$ is the force of gravity.
It can also be given as the difference between the actual weight and the apparent weight of the floating body.
Therefore, $F-b=W{W}_a=1400-900=500N$
That is, $500=V\times 998kg/m^3\times 9.8m/s^2$ = $0.051m^3$.
Hence, the volume of the rock is $5.1\times {10}^{-2}{m}^3$.