Question

1. A block of stone of mass 30 kg (S.G. 3) hangs from a cord and is completely immersed in water. Find the tension in the cord.

Answer 1

Here T is the tension in the cord, mg is the gravity force, Fa is the Archimedes' force. Also given that m = 30 kg and $S.G. = \dfrac{\rho_{stone}}{\rho_{water}}$, g = 9.8 m/s^2

Solution

As far as the stone does not move, the sum of up and down forces isp equal to zero. Thus:

$T + F_a = mg \Rightarrow T = mg - F_a.\\$

By definition, $F_a = \rho_{water}gV,$ where $V$ is the volume of stone: $V = \dfrac{m}{\rho_{stone}}.$

Putting all together, $T = mg - \rho_{water}g\dfrac{m}{\rho_{stone}} = mg(1-\dfrac{1}{S.G.})\\$ .

$T = 30\cdot 9.8 \cdot \dfrac{2}{3} = 196$

Answer. The tension in the cord is 196 Newtons.