Question 21:
easyA U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with \(12\text{ cm}\) of water in one arm and \(15\text{ cm}\) of spirit in other. The specific gravity of spirit is
At the interface level, the pressure on both sides must be equal: \(h_w \rho_w g = h_s \rho_s g\). Thus, \(\rho_s / \rho_w = h_w / h_s = 12 / 15 = 0.8\).
Question 22:
moderateA barometer is constructed using a liquid (density = $760 \text{ kg/m}^3$). What would be the height of the liquid column, when a mercury barometer reads $76 \text{ cm}$? (density of mercury = $13600 \text{ kg/m}^3$)
(2020-Covid)
Equating pressures, we get $h_1 \rho_1 g = h_2 \rho_2 g$. Substituting the given values, $$h_1 \times 760 = 0.76 \times 13600$$. Solving for $h_1$, we obtain $h_1 = 13.6 \text{ m}$.
Question 23:
moderateTwo non-mixing liquids of densities $\rho$ and $n\rho$ ($n > 1$) are put in a container. The height of each liquid is $h$. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $pL$ ($p < 1$) in the denser liquid. The density $d$ is equal to:
(2016 – I)
In equilibrium, the weight of the cylinder is balanced by the buoyant force from both liquids. $d \cdot A \cdot L \cdot g = \rho \cdot A \cdot (L - pL) \cdot g + n\rho \cdot A \cdot pL \cdot g$. Dividing by $A \cdot L \cdot g$, we get $d = \rho (1 - p) + n\rho p = \{1 + (n - 1)p\}\rho$.