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List of top Physics Questions on mechanical properties of fluid

A water tank is open at the top and has a hole of area \( 10^{-4} \, \text{m}^2 \) at the bottom. The height of the water column is 5 m. What is the speed of the water flowing out of the hole? (Take \( g = 10 \, \text{m/s}^2 \))
Water is being poured at the rate of 36 m$^3$/min into a cylindrical vessel whose circular base is of radius 3 meters. Then the water level in the cylinder increases at the rate of:
A fluid flows through a pipe with a varying cross-sectional area. If the velocity of the fluid is \( v_1 = 4 \, \text{m/s} \) at a point where the cross-sectional area is \( A_1 = 2 \, \text{m}^2 \), and the velocity at another point where the cross-sectional area is \( A_2 = 1 \, \text{m}^2 \) is \( v_2 \), what is the velocity \( v_2 \)?
A cylindrical pipe has a radius of \( 0.1 \, \text{m} \). If the speed of water flowing through the pipe is \( 2 \, \text{m/s} \), calculate the volume flow rate of water through the pipe.
A fluid of density \( 800 \, \text{kg/m}^3 \) is flowing through a pipe of varying cross-sectional area. The velocity of the fluid at point A is \( 2 \, \text{m/s} \), and the velocity at point B is \( 4 \, \text{m/s} \). If the cross-sectional area at point A is \( 1 \, \text{m}^2 \), find the cross-sectional area at point B.
A pipe has a radius of 2 cm at one end and 1 cm at the other end. The velocity of the water at the wider end is 5 m/s. What is the velocity of the water at the narrower end, assuming incompressible flow?
The magnifying power of a telescope is \( 9 \). When adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm. The ratio of the focal length of the objective lens to the focal length of the eyepiece is:
A rectangular loop of length \( 2.5 \) m and width \( 2 \) m is placed at \( 60^\circ \) to a magnetic field of \( 4 \) T. The loop is removed from the field in \( 10 \) sec. The average emf induced in the loop during this time is:
Five identical springs are used in the three configurations as shown in figure. The time periods of vertical oscillations in configurations (a), (b) and (c) are in the ratio:
\includegraphics[width=0.5\linewidth]{PH39.png}
Two vessels A and B are of the same size and are at the same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. \( P_A \) and \( P_B \) are the pressures of the gases in A and B respectively, then \( \frac{P_A}{P_B} \) is:
A solid metallic cube having total surface area \( 24 \, m^2 \) is uniformly heated. If its temperature is increased by \( 10^\circ C \), calculate the increase in volume of the cube.
Given: \( \alpha = 5.0 \times 10^{-4} \, C^{-1} \)
A pendulum of mass \( 1 \) kg and length \( l = 1 \) m is released from rest at an angle \( \theta = 60^\circ \). The power delivered by all the forces acting on the bob at angle \( \theta = 30^\circ \) will be (Take, \( g = 10 \) m/s\( ^2 \)):