Question

A block of silver of mass $4kg$ hanging from a string is immersed in a liquid of relative density $0.72$. If relative density of silver is $10$, then tension in the string will be

• A. 37.12 N
• B. 42 N
• C. 73 N
• D. 21 N

Answer 1

Answer: (A)

Let ${\rho }_S$ and ${\rho }_L$ be the densities of silver and liquid, respectively, and $m$ and $V$ be the mass and volume, respectively, of the silver block. Therefore,
Tension in the string $=mg$ - buoyant force
$\Rightarrow T={\rho }_{S}Vg-{\rho }_{L}Vg=\left({\rho }_S-{\rho }_L\right)Vg$
Also, $V=\frac{m}{{\rho }_S}$
$\therefore T=\left(\frac{{\rho }_S-{\rho }_L}{{\rho }_S}\right)mg$
$=\frac{(10-0.72)\times 10^3}{10\times 10^3}\times 4\times 10$
$=37.12N$