In a $U-$tube as shown in figure, water and oil are in the left side and right side of the tube respectively. The helghts from the bottom for water and oil columns are $15\; \mathrm{cm}$ and $20\; \mathrm{cm}$ respectively. The density of the oil is......$kg/{m}^{3}$
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Sixty four spherical rain drops of equal size are falling vertically through air with terminal velocity $1.5\, m/s$. All of the drops coalesce to form a big spherical drop, then terminal velocity of big drop is ........... $m/s$
The 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 ........ $cm$
An ice cube contains a large air bubble. The cube is floating on the horizontal surface of water contained in a trough. What will happen to the water level, when the cube melts?
A cylindrical vessel open at the top is $20$ $cm $ high and $10$ $cm$ in diameter. A circular hole whose cross-sectional area $1$ $cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate $100$ $cm^3$ $s^{^{-1}}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g$ $=$ $1000 $ $cm s^{^{-2}})$
$Assertion :$ For Reynold’s number $Re > 2000$, the flow of fluid is turbulent.
$Reason :$ Inertial forces are dominant compared to the viscous forces at such high Reynold’s numbers.
An open-ended U-tube of uniform cross-sectional area contains water (density $10^3 kg m ^{-3}$ ). Initially the water level stands at $0.29 m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 kg m ^{-3}$ is added to the left arm until its length is $0.1 m$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-
A copper ball of radius $'r'$ travels with a uniform speed $'v'$ in a viscous fluid. If the ball is changed with another ball of radius $'2r'$ , then new uniform speed will be