Question

A metallic sphere of mass $3\text{kg}$ is held by a string and is completely immersed in a liquid of relative density $0.8$. The relative density of the metallic sphere is $10$. What is the tension in the string? Take $g=10{\text{ms}}^{-2}$

• A. $18.7\text{N}$
• B. $42.5\text{N}$
• C. $32.7\text{N}$
• D. $27.6\text{N}$

Answer 1

The correct option is D $27.6\text{N}$

At equilibrium,
$T+F_t=Mg$,
Here, $T\to$ tension in the string
$F_t\to$ thrust force


$\Rightarrow T+{\rho }_{l}gV={\rho }_{m}gV$

Given, ${\rho }_l=0.8{\rho }_w$ & ${\rho }_m=10{\rho }_w$
$\Rightarrow T+0.8{\rho }_{w}gV=10{\rho }_{w}gV$
$\Rightarrow T=9.2{\rho }_{w}gV$
$\Rightarrow T=9.2{\rho }_{w}g\times \frac{m}{{\rho }_m}$
$\Rightarrow T=9.2{\rho }_{w}g\times \frac{3}{10{\rho }_w}$
$\Rightarrow T=27.6\text{N}$