Question:
A solid cylinder of length \(l\) and cross-sectional area A is immersed such that it floats with its axis vertical at the liquid-liquid interface with length \(\frac{l}{3}\) in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere, having pressure \(P_{0}\). The density of a solid cylinder is
A solid cylinder of length \(l\) and cross-sectional area A is immersed such that it floats with its axis vertical at the liquid-liquid interface with length \(\frac{l}{3}\) in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere, having pressure \(P_{0}\). The density of a solid cylinder is
Show Hint
In equilibrium the weight equals the total buoyant force from both liquids. Atmospheric pressure cancels out.
Updated On: Nov 12, 2026
- \(\frac{3\rho }{2}\)
- \(\frac{2\rho }{3}\)
- \(\frac{5\rho }{3}\)
- \(\frac{3\rho }{5}\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
The cylinder floats fully immersed, with \(\frac{l}{3}\) in the denser liquid of density \(3\rho\) and \(\frac{2l}{3}\) in the lighter liquid of density \(\rho\).
Step 2: Equilibrium
Weight = buoyant force:
\(\sigma Alg=\dfrac{l}{3}A(3\rho)g+\dfrac{2l}{3}A\rho g\)
Step 3: Calculation
\(\sigma=\rho+\dfrac{2\rho}{3}=\dfrac{5\rho}{3}\)
Final Answer:
The density of the cylinder is \(\frac{5\rho}{3}\). \[ \boxed{\text{(C) }\dfrac{5\rho}{3}} \]
The cylinder floats fully immersed, with \(\frac{l}{3}\) in the denser liquid of density \(3\rho\) and \(\frac{2l}{3}\) in the lighter liquid of density \(\rho\).
Step 2: Equilibrium
Weight = buoyant force:
\(\sigma Alg=\dfrac{l}{3}A(3\rho)g+\dfrac{2l}{3}A\rho g\)
Step 3: Calculation
\(\sigma=\rho+\dfrac{2\rho}{3}=\dfrac{5\rho}{3}\)
Final Answer:
The density of the cylinder is \(\frac{5\rho}{3}\). \[ \boxed{\text{(C) }\dfrac{5\rho}{3}} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Buoyancy and Floatation Questions
A body is floating in oil. The density of the oil is \( \rho_{\text{oil}} \) and the density of the body is \( \rho_{\text{body}} \). If the body is partially submerged, what is the fraction of the body's volume submerged in the oil?
Given:
\( \rho_{\text{oil}} \) = density of the oil,
\( \rho_{\text{body}} \) = density of the body.- A small metal sphere of density $\rho$ is dropped from height $h$ into a jar containing liquid of density $\sigma (\sigma > \rho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces)
- A small metal sphere of density $\rho$ is dropped from height $h$ into a jar containing liquid of density $\sigma (\sigma > \rho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces)
- A vessel contains oil (density \(= 0.8\text{ gm}/\text{cm}^3\)) over mercury (density \(= 13.6\text{ gm}/\text{cm}^3\)). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in \(\text{gm}/\text{cm}^3\) is
- A rectangular block of mass 'm' and cross-sectional area 'A' floats on a liquid of density '\(ρ\)'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency (g=acceleration due to gravity)
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions