WBJEE · Physics · Mechanical Properties of Fluids
A piece of granite floats at the interface of mercury and water contained in a beaker as in figure. If the densities of granite, water and mercury are \(\rho, \rho_1\) and \(\rho_2\) respectively, the ratio of the volume of granite in water to the volume of granite in mercury is
- A \(\frac{\rho_2-\rho}{\rho-\rho_1}\)
- B \(\frac{\rho_2+\rho}{\rho_1+\rho}\)
- C \(\frac{\rho_1 \rho_2}{\rho}\)
- D \(\frac{\rho_1}{\rho_2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\rho_2-\rho}{\rho-\rho_1}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & V_1 \rho_1 g+V_2 \rho_2 g=V \rho g \\ & \Rightarrow V_1 \rho_1 g+V_2 \rho_2 g=\left(V_1+V_2\right) \rho g \\ & \Rightarrow V_1 \rho_1 g-V_1 \rho g=V_2 \rho g-V_2 \rho_2 g, \Rightarrow V_1\left(\rho-\rho_1\right)=V_2\left(\rho_2-\rho\right) \\ & \Rightarrow…
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