Question

A hollow sphere of mass $M$ and radius $R$ is immersed in a tank of water (density ${\rho }_{\text{w}}$ ). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle $45^{\circ }$ with the horizontal as shown in the diagram. The tension $T_1$ in the wire is

• A. $\frac{\frac{4}{3}\pi R^3{\rho }_{\text{w}}\text{g}-M\text{g}}{\sqrt{2}}$
• B. $\frac{2}{3}\pi R^3{\rho }_{\text{w}}\text{g}-M\text{g}$
• C. $\frac{\frac{4}{3}\pi R^3{\rho }_{\text{w}}\text{g}-M\text{g}}{2}$
• D. $\frac{4}{3}\pi R^3{\rho }_{\text{w}}\text{g}+M\text{g}$

Answer 1

Answer: (A)

$\therefore \sqrt{2}{T}_1+M\text{g}=\frac{4}{3}\pi R^3{\rho }_{\text{w}}\text{g}$
$\therefore T_1=\frac{\frac{4}{3}\pi R^3{\rho }_{\text{w}}\text{g}-M\text{g}}{\sqrt{2}}$