The terminal velocity of a copper ball of radius $5\,mm$ falling through a tank of oil at room temperature is $10\,cm\,s ^{-1}$. If the viscosity of oil at room temperature is $0.9\,kg\,m ^{-1} s ^{-1}$, the viscous drag force is :
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A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\omega $then
The surface of water in a water tank of cross section area $750\,cm ^2$ on the top of a house is $h m$. above the tap level. The speed of water coming out through the tap of cross section area $500\,mm ^2$ is $30\,cm / s$. At that instant, $\frac{d h}{d t}$ is $x \times 10^{-3} m / s$. The value of $x$ will be $.............$.
Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is $36 g $ and its density is $9 g / cm^3$. If the mass of the other is $48 g$, its density in $g / cm^3$ is
A large tank is filled with water (density $=$ $10^3 $ $kg/m^3$).A small hole is made at a depth $10$ $m$ below water surface. The range of water issuing out of the hole is Ron ground. What extra pressure must be applied on the water surface so that the range becomes $2R $ (take $1$ $atm$ $=$ $10^5$ $Pa$ and $g$ $=$ $10$ $m/s^2):$ ...... $atm$
In the figure shown, a liquid is flowing through a tube at the rate of $0.1\, m^3/sec$. The tube is branched into two semicircular tubes of cross-sectional area $A/3$ and $2A/3$. The velocity of liquid at $Q$ is ......... $ m/sec$ (The cross-section of the main tube $= A =10^{-2}\, m^2$ and $v_p = 20\, m/sec$)
A piston of cross-section area $100\, cm^2$ is used in a hydraulic press to exert a force of $107\, dynes$ on the water. The cross-sectional area of the other piston which supports an object having a mass $2000 \,kg$. is
An aeroplane of mass $3 \times 10^4\, kg$ and total wing area of $120\, m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is $(g=10\,m/s^2)$