Question

When a body is made to float on the surface of the liquid it was found it started sinking towards the bottom. If the mass of the body is $\text{m}$, weight of the body is $\text{W}$ and the buoyant force acting on the body $F_b$. What is the acceleration with which the body will sink towards the bottom?

• A. $\frac{\text{W}-F_b}{\text{m}}$
• B. $\frac{\text{m}}{F_b-\text{W}}$
• C. $\frac{\text{m}}{\text{W}-F_b}$
• D. $\frac{F_b-\text{W}}{\text{m}}$

Answer 1

The correct option is A $\frac{\text{W}-F_b}{\text{m}}$

The body has mass $\text{m}$ and will sink with some acceleration, say $\text{a}$.

From the free body diagram, we see that the net force is equal to $\text{W}-F_b$

From Newton's second law, we can infer that the net force is equal to mass times acceleration

$\text{W}-F_b=\text{m}\times \text{a}$

Or, $\text{a}=\frac{\text{W}-F_b}{\text{m}}$