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.) ........... $cm\,s^{-1}$
Medium
Download our app for free and get started
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 $\quad \mathrm{v}_{2 \mathrm{x}}=\left(\mathrm{v}_{\mathrm{r}}\right) \times 4=4 \mathrm{cm} / \mathrm{s}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The area of cross-section of the wider tube shown in figure is $800$ $cm^2$. If a mass of $12$ $ kg $ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes is ........ $cm$View Solution
- 2$Assertion :$ In a pressure cooker the water is brought to boil. The cooker is then remove from the stove. Now on removing the lid of the pressure cooker, the water starts boiling against.View Solution
$Reason :$ The impurities in water bring down its boiling point - 3A cylinder stands vertical in two immiscible liquids of densities $\rho$ and $2 \rho$. The height of two liquids are shown. Find the difference in pressure at point $A$ and $B$View Solution
- 4Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is $3$ : $2$. Then the ratio of velocities at entry and exit of liquid isView Solution
- 5A submarine has a window of area $30 \times 30 \,cm ^2$ on its ceiling and is at a depth of $100 \,m$ below sea level in a sea. If the pressure inside the submarine is maintained at the sea-level atmosphere pressure, then the force acting on the window is ............. $N$ (consider density of sea water $=1.03 \times 10^3 \,kg / m ^3$, acceleration due to gravity $=10 \,m / s ^2$ )View Solution
- 6If the terminal speed of a sphere of gold ( density $= 19.5 kg/m^3$) is $0.2\ m/s$ in a viscous liquid (density $= 1.5\ kg/m^3$ ), find the terminal speed (in $m/s$) of a sphere of silver (density $= 10.5\ kg/m^3$) of the same size in the same liquid ...... $m/s$View Solution
- 7A space $2.5\ cm$ wide between two large plane surfaces is filled with oil. Force required to drag very thin plate of area $0.5\ m^2$ just midway the surfaces at a speed of $0.5\ m/sec$ is $1\ N$ The coefficient of viscosity in $kg-s/m^2$ is :View Solution
- 8A candle of diameter $ d$ is floating on a liquid in a cylindrical container of diameter $D $ $(D>>d)$ as shown in figure. If it is burning at the rate of $2$ cm/hour then the top of the candle willView Solution
- 9The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are $v$ and $2v$ respectively. The density of air is $\rho $ and surface area of wing is $A$ . The dynamic lift on the wing isView Solution
- 10In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius $2.0 \times 10^{-5}\, {m}$ and density $1.2 \times 10^{3} \,{kgm}^{-3}$ ? Take viscosity of liquid $=1.8 \times 10^{-5}\, {Nsm}^{-2} .$ (Neglect buoyancy due to air).View Solution