A solid block of volume V = 10^-3 m³ and density d = 800 kg/m³ is tied to one end of a string, the other end of which is tied to the bottom of the vessel. The vessel contains 2 immiscible liquids of densities $ρ_{1}$ = 1000 kg/m³ and $ρ_{2}$ = 1500 kg/m³ . The solid block is immersed with 2/5th of its volume in the liquid of higher density and 3/5th in the liquid of lower density. The vessel is placed in an elevator which is moving up with an acceleration of a=g/2. The tension in the string is _____. [g = 10 m/s²]

Moderate

Solution

Upthrust on the block
$\begin{matrix} = \frac{2}{5} V \times 1500 (g + \frac{g}{2}) + \frac{3}{5} V \times 1000 \times (g + \frac{g}{2}) \\ = 1800 \times 10^{- 3} \times 10 = 18 N \end{matrix}$
weight of the block $= 10^{- 3} \times 800 \times (g + \frac{g}{2}) = 12 N$
So Tension in the string $= Th - m g = 18 - 12 = 6 N$

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