A spherical solid ball of volume V is made of a material of density ρ ₁ . It is falling through a

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9-1.Fluid Mechanics

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A spherical solid ball of volume $V$ is made of a material of density $\rho _1$. It is falling through a liquid of density $\rho _2(\rho _2 < \rho _1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v,$ i.e., $F_{viscous} = -k\upsilon ^2 (k > 0)$. The terminal speed of the ball is

$\sqrt {\frac{{Vg({\rho _1} - {\rho _2})}}{k}} $

$\frac{{Vg{\rho _1}}}{k}$

$\sqrt {\frac{{Vg{\rho _1}}}{k}} $

$\frac{{Vg({\rho _1} - {\rho _2})}}{k}$

Solution

The force acting on the ball are gravity force. buoyancy force and viscous force. When ball acquires terminal speed. it is in dynamic equilibrium, let terminal speed of ball is $v_{T}$

So. $\mathrm{V} \rho_{2} \mathrm{g}+\mathrm{kv}_{\mathrm{T}}^{2}=\mathrm{V} \rho_{1} \mathrm{g}$

$v_{T}=\sqrt{\frac{V\left(\rho_{1}-\rho_{2}\right) g}{k}}$

Standard 11

Physics

A wind with speed $40\,m/s$ blows parallel to the roof of a house. The area of the roof is $250\,m^2.$ Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $(\rho _{air} = 1.2\,kg/m^3)$

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A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho $ . sphere is moving horizontally with an acceleration $2\ g$ , where $g$ is acceleration due to gravity in the space. If minimum pressure of liquid is $P_0$ , then pressure at the centre of sphere is

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A liquid $X$ of density $3.36\, g/cm^3$ is poured in a $U$ -tube upto $10\, cm$ height, which contains $Hg.$ Another liquid $Y$ is poured in left arm with height $8\, cm$. Upper levels of $X$ and $Y$ are same. ………… $gm/cc$ is density of $Y$ .
(Density of $Hg = 13.6 \times 10^3\, kg/m^3$)

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An $L-$ shaped glass tube is just immersed in flowing water towards tube as shown. If speed of water current is $V$, then the height $h$ upto which water rises will be

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Solution

Similar Questions

A wind with speed $40\,m/s$ blows parallel to the roof of a house. The area of the roof is $250\,m^2.$ Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $(\rho _{air} = 1.2\,kg/m^3)$

A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho $ . sphere is moving horizontally with an acceleration $2\ g$ , where $g$ is acceleration due to gravity in the space. If minimum pressure of liquid is $P_0$ , then pressure at the centre of sphere is

A liquid $X$ of density $3.36\, g/cm^3$ is poured in a $U$ -tube upto $10\, cm$ height, which contains $Hg.$ Another liquid $Y$ is poured in left arm with height $8\, cm$. Upper levels of $X$ and $Y$ are same. ………… $gm/cc$ is density of $Y$ . (Density of $Hg = 13.6 \times 10^3\, kg/m^3$)

An $L-$ shaped glass tube is just immersed in flowing water towards tube as shown. If speed of water current is $V$, then the height $h$ upto which water rises will be

A tank is filled upto a height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get maximum range $x_m$ a small hole is punched at a distance of $y$ from the free surface of the liquid. Then

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A liquid $X$ of density $3.36\, g/cm^3$ is poured in a $U$ -tube upto $10\, cm$ height, which contains $Hg.$ Another liquid $Y$ is poured in left arm with height $8\, cm$. Upper levels of $X$ and $Y$ are same. ………… $gm/cc$ is density of $Y$ .
(Density of $Hg = 13.6 \times 10^3\, kg/m^3$)