A solid block owf volume V=10^-3m³ 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 (in N) is ________. (g = 10 m/s²)

Difficult

Solution

Upthrust on the block
$\begin{aligned} \begin{array}{l} U = \frac{2}{5} V \times 1500 (g + \frac{g}{2}) + \frac{3}{5} V \times 1000 \times (g + \frac{g}{2}) \\ = 1800 \times 10^{- 3} \times 10 = 18 N \end{array} \\ Weight of the block = 10^{- 3} \times 800 \times (g + \frac{g}{2}) = 12 N \\ So, tension in the string = U - m g = 18 - 12 = 6 N \end{aligned}$

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