Two uniform solid balls of same density and of radii r and 2r are dropped in air and fall vertically

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9-1.Fluid Mechanics

medium

Two uniform solid balls of same density and of radii $r$ and $2r$ are dropped in air and fall vertically downwards. The terminal velocity of the ball with radius $r$ is $1\,cm\,s^{-1}$ , then find the terminal velocity of the ball of radius $2r$ (neglect bouyant force on the balls.) ........... $cm\,s^{-1}$

$0.5$

$4$

$1$

$2$

Solution

At equilibrium

$\mathrm{mg}=6 \pi \eta \mathrm{rv} \quad$ or $\quad \rho \frac{4 \pi}{3} \mathrm{r}^{3} \mathrm{g}=4 \pi \eta \mathrm{rV}$

$\therefore \quad \frac{v_{\mathrm{r}}}{\mathrm{v}_{2 \mathrm{r}}}=\frac{(\mathrm{r})^{2}}{(2 \mathrm{r})^{2}} \quad$ or $\quad \mathrm{v}_{2 \mathrm{x}}=\left(\mathrm{v}_{\mathrm{r}}\right) \times 4=4 \mathrm{cm} / \mathrm{s}$

Standard 11

Physics

A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P ( r )$ is the pressure at $r ( r < R )$, then the correct option$(s)$ is(are)

$(A)$ $P ( I =0)=0$ $(B)$ $\frac{ P ( r =3 R / 4)}{ P ( r =2 R / 3)}=\frac{63}{80}$

$(C)$ $\frac{ P ( r =3 R / 5)}{ P ( r =2 R / 5)}=\frac{16}{21}$ $(D)$ $\frac{ P ( r = R / 2)}{ P ( r = R / 3)}=\frac{20}{27}$

medium

(IIT-2015)

Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.

medium

A lead shot of $1mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$. with distance covered is represented by

medium

(AIIMS-2003)

Which of the following option correctly describes the variation of the speed $v$ and acceleration $'a'$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv,$ where $'k'$ is a constant, on the body? (Graphs are schematic and not drawn to scale)

medium

(JEE MAIN-2016)

A solid metallic sphere of radius $r$ is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following?

hard

Solution

Similar Questions

Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.

A lead shot of $1mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$. with distance covered is represented by

Which of the following option correctly describes the variation of the speed $v$ and acceleration $'a'$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv,$ where $'k'$ is a constant, on the body? (Graphs are schematic and not drawn to scale)

A solid metallic sphere of radius $r$ is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following?

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