Fluid Mechanics – JEE Advanced Previous Year Questions with Solutions

JEE Advanced Previous Year Questions of Physics with Solutions are available at eSaral. Practicing JEE Advanced Previous Year Papers Questions of Physics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas.

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Paragraph for Questions no. 3 to 5

When liquid medicine of density  is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

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Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.

Paragraph for Questions 24 to 25

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere.

Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $\mathrm{u}_{0}$. Which of the following statements is (are) true ?

(A) The resistive force of liquid on the plate is inversely proportional to h

(B) The resistive force of liquid on the plate is independent of the area of the plate

(C) The tangential (shear) stress on the floor of the tank increases with $\mathrm{u}_{0}$.

(D) The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid.

#sol# (A,C,D)

Viscous force is given by F = $-\eta \mathrm{A} \frac{\mathrm{dv}}{\mathrm{dy}}$ since h is very small therefore, magnitude of viscous force is given by

$\mathrm{F}=\eta \mathrm{A} \frac{\Delta \mathrm{v}}{\Delta \mathrm{y}}$

$\therefore \mathrm{F}=\frac{\eta \mathrm{Au}_{0}}{\mathrm{h}} \Rightarrow \mathrm{F} \propto \eta \& \mathrm{F} \propto \mathrm{u}_{0} \quad ; \quad \mathrm{F} \propto \frac{1}{\mathrm{h}}, \mathrm{F} \propto \mathrm{A}$

Since plate is moving with constant velocity, same force must be acting on the floor.