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)

$∴ \, \, \, \sqrt{2} \, T_{1}+M\text{g}=\frac{4}{3}\pi R^{3}\rho _{\text{w}}\text{g}$
$∴ \, \, T_{1}= \, \frac{\frac{4}{3} \pi R^{3} \rho _{\text{w}} \text{g} - M \text{g}}{\sqrt{2}}$