Question

If a body floats with $(m/n{)}^{th}$ of its volume above the surface of water, then the relative density of the material of the body is:

• A. $\frac{(n-m)}{n}$
• B. $\frac{m}{n}$
• C. $\frac{n}{m}$
• D. $\frac{(n-m)}{m}$

Answer 1

Answer: (A)

$\frac{(n-m)}{n}$

As body floats with $(\frac{m}{n}{)}^{th}$ volume above.

Volume of liquid displaced $=[1-(\frac{m}{n}\left)\right]V$

$\therefore$ weight of cube $=$ weight of displaced liquid

$\Rightarrow V{\rho }_s=[1-(\frac{m}{n}\left)\right]V\rho$

$\frac{{\rho }_s}{\rho }=[1-(\frac{m}{n}\left)\right]=\left[\frac{n-m}{n}\right]$