A spherical ball of radius $r$ and relative density $0.5$ is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is : (where $\rho $ is the density of water)
A spherical ball of radius $r$ and relative density $0.5$ is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is : (where $\rho $ is the density of water)
- A
$\frac{5}{{12}}\pi {r^4}\rho g$
- B
$0.5\rho rg$
- C
$\frac{4}{3}\pi {r^3}\rho g$
- D
$\frac{2}{3}\pi {r^4}\rho g$
Similar Questions
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A:$ When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.
Reason $R:$ A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements, choose the most appropriate answer from the options given below
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A:$ When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.
Reason $R:$ A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements, choose the most appropriate answer from the options given below
- [JEE MAIN 2023]
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A uniform rod of density $\rho $ is placed in a wide tank containing a liquid of density ${\rho _0}({\rho _0} > \rho )$. The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position the rod makes an angle $\theta $ with the horizontal
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A jar is filled with two non-mixing liquids $1$ and $2$ having densities $\rho_1$ and, $\rho_2$ respectively. A solid ball, made of a material of density $\rho_3$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for $\rho_1 , \rho_2$ and $\rho_3$?
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