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  4. 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 is (k/18) N. The value of k is.(Given, g=10 ms -2 )

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Q. 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 is $\frac{k}{18} N$. The value of $k$ is_____.(Given, $g=10\, ms ^{-2}$ )Physics Question Image

Mechanical Properties of Fluids

Solution:

image
$T+m g=B_{F_{1}}$
Or $T+(0.8)(250) g=(250) \rho_{L} g$ ...(i)
$T+B_{F_{2}}=m_{2} g$
Or $T+(250)\left(\rho_{L}\right)(g)=(1.2)(250)(g)$ ...(ii)
From equations (i) and (ii), $T=0.5 N$
$\therefore \frac{k}{18}=\frac{1}{2}$
$\Rightarrow k=9$