First slide

Pressure in a fluid-mechanical properties of fluids

Question

Two spheres each of volume 250 cc but of relative densities 0.8 and 1.2 are connected by a string and the combination is immersed in a liquid in vertical position as shown in the figure. The tension in the string $\frac{k}{18}$ N. The value of k is ________. (Given, g=10 ms^-2)

Moderate

Solution

$\begin{array}{l} T + m g = B_{F_{1}} \\ Or T + (0.8) (250) g = (250) ρ_{L} g . . . . . . (i) \\ T + B_{F_{2}} = m_{2} g \\ Or T + (250) (ρ_{L}) (g) = (1.2) (250) (g) . . . . . . . . (ii) \\ From equations (i) and (ii), T = 0.5 N \\ ∴ \frac{k}{18} = \frac{1}{2} \Rightarrow k = 9 \end{array}$

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