Question

A wooden block of mass $8kg$ is tied to a string attached to the bottom of a tank. The block is completely inside the water. Relative density of wood is $0.8$. Taking $g=10m/s^2$, what is the tension in the string?

• A. $100N$
• B. $80N$
• C. $50N$
• D. $20N$

Answer 1

Answer: (D)

$20N$

as seen from diagram, we have
$T+mg=F_b$
$\Rightarrow T=F_b-mg$
$\Rightarrow T=V{\rho }_{water}g-mg$ where $V=$volume of water displaced$=$ volume of wooden block
$\Rightarrow T=\frac{m}{{\rho }_{wood}}{\rho }_{water}g-mg$
$\Rightarrow T=\frac{m}{k{\rho }_{water}}{\rho }_{water}g-mg$
$\Rightarrow T=mg(\frac{1}{k}-1)=8\times 10(\frac{1}{0.8}-1)=20N$