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 $[takeg=10m/s^2]$

• A. $37.12N$
• B. $42.21N$
• C. $73.7N$
• D. $21.13N$

Answer 1

The correct option is A $37.12N$

Let ${\rho }_s$, ${\rho }_l$ be the density of silver and liquid.
Let $m_s$ and $V_s$ be the mass and volume of the silver block.

In equilibrium, the sum of tension and buoyant force is equal to the weight of the silver block. Hence
$T+V_s\times {\rho }_l\times g=V_s\times {\rho }_s\times g$
$\therefore T=({\rho }_s-{\rho }_l)V_{s}g=({\rho }_s-{\rho }_l)m_s{\rho }_{s}g$
$\therefore T=\frac{{\rho }_s-{\rho }_l}{{\rho }_s}{m}_{s}g$
$\therefore T=\frac{10-0.72}{10}4\times 10=37.12N$