Fluid Mechanics JEE Main PYQs, 2020 to 2025

A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}$ while falling under gravity through an oil of density $925 \mathrm{~kg} \mathrm{~m}^{-3}$. Take density of steel as $7825 \mathrm{~kg} \mathrm{~m}^{-3}$ and g as $9.8 \mathrm{~m} / \mathrm{s}^2$. The viscosity of the oil in SI unit is

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?

(Given: density of water = 1000 kg m^-3)

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

The surface of water in a water tank of cross section area $750 \mathrm{~cm}^{2}$ on the top of a house is $h \mathrm{~m}$ above the tap level. The speed of water coming out through the tap of cross section area $500 \mathrm{~mm}^{2}$ is $30 \mathrm{~cm} / \mathrm{s}$. At that instant, $\frac{d h}{d t}$ is $x \times 10^{-3} \mathrm{~m} / \mathrm{s}$. The value of $x$ will be ____________.