A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $\mathrm{M}$ and density $\rho $ is suspended by a massless spring of spring constant $\mathrm{k}$. This block is submerged inside into the water in the vessel. What is the reading of the scale ?
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $\mathrm{M}$ and density $\rho $ is suspended by a massless spring of spring constant $\mathrm{k}$. This block is submerged inside into the water in the vessel. What is the reading of the scale ?
Take a figure into consideration.
The scale is adjusted to zero. Therefore, when a block suspended to a spring is immersed in water, then the reading of the scale will be equal to the upthrust on the block due to water. Upthrust experienced by the block = weight of displaced water
$=(\mathrm{V}) \rho_{\mathrm{w}} \mathrm{g}(\mathrm{V}=$ volume of block $)$
$=\frac{m}{\rho} \rho_{w} g \quad\left(\rho_{w}=\right.$ density of water $)$
$=\left(\frac{\rho_{\mathrm{w}}}{\rho}\right) m g(\rho=$ density of block $)$
Similar Questions
An object is fitted in a hole at base of a container as shown in figure, the force due to liquid on object is (Assume no leakage of water, volume of object inside container is $V$ and density of liquid is $\rho $ )
An object is fitted in a hole at base of a container as shown in figure, the force due to liquid on object is (Assume no leakage of water, volume of object inside container is $V$ and density of liquid is $\rho $ )
The weight of an empty balloon on a spring balance is $w_1$. The weight becomes $w_2$ when the balloon is filled with air. Let the weight of the air itself be $w$ .Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside $\&$ outside the balloon. Then :
The weight of an empty balloon on a spring balance is $w_1$. The weight becomes $w_2$ when the balloon is filled with air. Let the weight of the air itself be $w$ .Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside $\&$ outside the balloon. Then :
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]
Write and prove Archimedes principle.
Write and prove Archimedes principle.
A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is
A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is
- [JEE MAIN 2013]