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9-1.Fluid Mechanics
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A hollow sphere of mass $M$ and radius $r$ is immersed in a tank of water (density $\rho$$_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 $45^o$ with the horizontal as shown in the figure. The tension $T_1$ in the wire is :
A
$\frac{{\frac{4}{3}\pi \,{R^3}{\rho _w}g - Mg}}{{\sqrt 2 }}$
B
$\frac{2}{3}\pi \,{R^3}{\rho _w}g - Mg$
C
$\frac{{\frac{4}{3}\pi \,{R^3}{\rho _w}g - Mg}}{2}$
D
$\frac{4}{3}\pi \,{R^3}{\rho _w}g + Mg$
Solution
$2 T \sin 45^{\circ}=B-W$
$2 T \times \frac{1}{\sqrt{2}}=\frac{4}{3} \pi R^{3} \rho_{w} g-M g \quad \Rightarrow T=\frac{\frac{4}{3} \pi R^{3} \rho_{w} g-M g}{\sqrt{2}}$
Standard 11
Physics
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