Velocity of Efflux and Torricelli's law PYQs: JEE Mains Physics

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1. 1. A cylindrical vessel of \(40\) cm radius is completely filled with water and its capacity is \(528\) dm\(^3\) (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at \(70\) cm below the top of water level, then horizontal range of water falling on the ground in the beginning is __________ cm. 2026 Hard
2. 2. Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area \(0.5 \mathrm{~m}^2\). It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)\) 2025 Hard
3. 3. Consider a cylindrical tank of radius \(1 m\) is filled with water. The top surface of water is at \(15\,m\) from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of \(5\,m\) from the bottom. A force of \(5 \times 10^{5} N\) is applied an the top surface of water using a piston. The speed of efflux from the hole will be. (given atmospheric pressure \(P_{A}=1.01 \times 10^{5}\,Pa\), density of water \(\rho_{ w }=1000\,kg / m ^{3}\) and gravitational acceleration \(g=10\,m / s ^{2}\) )
   2022 Hard
4. 4. The area of cross-section of a large tank is \(0.5 \; m ^{2}\). It has a narrow opening near the bottom having area of cross-section \(1 \; cm ^{2}\). A load of \(25 \; kg\) is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is \(40 \; cm\) above the bottom, will be \(\dots \; cms ^{-1}\). \(\left[\right.\) Take \(\left.g =10 \; ms ^{-2}\right]\) 2022 Medium
5. 5. The water is filled upto height of \(12\, {m}\) in a tank having vertical sidewalls. A hole is made in one of the walls at a depth \('{h}'\) below the water level. The value of \('h'\) for which the emerging stream of water strikes the ground at the maximum range is \(.....\,{m}\). 2021 Medium
6. 6. A liquid of density \(\rho \) is coming out of a hose pipe of radius \(a\) with horizontal speed \(v\) and hits a mesh. \(50\%\) of the liquid passes through the mesh unaffected. \(25\%\) looses all of its momentum and \(25\%\) comes back with the same speed. The resultant pressure on the mesh will be 2019 Hard
7. 7. The top of a water tank is open to air and its water level is maintained. It is giving out \(0.74\,m^3\) water per minute through a circular opening of \(2\,cm\) radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ \(m\) 2019 Medium
8. 8. Water flows into a large tank with flat bottom at the rate of \({10^{ - 4}}\,{m^3}{s^{ - 1}}\). Water is also leaking out of a hole of area \(1\, cm^2\) at its bottom. If the height of the water in the tank remains steady, then this height is........ \(cm\) 2019 Medium
9. 9. A cylindrical vessel of cross-section \(A\) contains water to a height \(h\) . There is a hole in the bottom of radius \('a'\) . The time in which it will be emptied is 2014 Hard

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