Exams › JEE Advanced › Physics
A container of cross-sectional area A has a small hole of area a = A/3 at the bottom. Initially liquid is filled to height h from the base. As liquid flows out, which of the following is correct?
- The level of liquid in the container falls at a rate of sqrt(g*h/4) m/s
- The magnitude of acceleration of the top liquid surface is g/8 m/s²
- The acceleration of the top liquid surface is g/3 m/s²
- None of these
Correct answer: The magnitude of acceleration of the top liquid surface is g/8 m/s²
Solution
Rate of fall of liquid surface from continuity, then differentiate to get acceleration. With a = A/3, the rate equations and acceleration can be computed from the Torricelli equation.
Related JEE Advanced Physics questions
- A glass partially filled with water is attached to a wedge that slides without friction down a large inclined plane of angle alpha. The mass of the inclined plane is M and the combined mass of the wedge, glass, and water is m. In the absence of motion the water surface is horizontal. Choose the correct option(s).
- A solid sphere of mass 1 kg and radius 1 m falls vertically through a viscous liquid in gravity-free space. At a certain instant its speed is 2 m/s. Given that the coefficient of viscosity is 1/(12*pi) N*s/m², find the time (in seconds) after which the speed reduces to 1 m/s.
- An ice cube floats in water, and a layer of oil (less dense than water) is poured on top of the water. As the ice melts completely, what happens to (i) the level of the water-oil interface, and (ii) the uppermost level of the oil?
- A solid object is fully submerged in a liquid. The net force exerted by the liquid on the solid will:
- A cylindrical vessel containing water is rotated about its vertical axis with constant angular velocity omega. Find (a) the shape of the free surface of the water, and (b) the water pressure distribution over the bottom of the vessel as a function of radius r, given that the pressure at the center of the bottom is p0.
- Statement-1: A fast jet of water from a hose spreads out like a fountain when the hose is pointed vertically upward, but it narrows down when pointed vertically downward. Statement-2: For the steady flow of an incompressible fluid, the volume flow rate stays constant along the stream. Select the correct option.
⚔️ Practice JEE Advanced Physics free + battle 1v1 →