Fluids – JEE First

Archimedes’ principle with worked examples

August 7th, 2022jeefirst0 Comments

This article reviews Archimedes’ principle and elaborates on the idea with three fully solved examples. The reader is encouraged to attempt the problems on their own before checking the solution.

Consider a container $A$ of fluid at rest, as shown in the figure below. Since the fluid is at rest the net force on any part of the fluid is zero. Let us draw an imaginary boundary around some region of the fluid, as shown in the figure. This parcel of fluid has a weight $\rho_{\rm fl} V g$ , where $\rho_{\rm fl}$ is the density of the fluid and $V$ is the volume of the parcel. …

Buoyancy of connected objects

July 16th, 2022jeefirst0 Comments

JEE Advanced 2013 Paper 1, Question 12

A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$ . The other end of the spring is connected to another solid sphere of radius $R$ and density $3 \rho$ . The complete arrangement is placed in a liquid of density $2 \rho$ and is allowed to reach equilibrium. The correct statement(s) is (are)

the net elongation of the spring is $\frac{4 \pi R^{3} \rho g}{3 k}$ .
the net elongation of the spring is $\frac{8 \pi R^{3} \rho g}{3 k}$
the light sphere is partially submerged.
the light sphere is completely submerged.

Solution

Recall that the buoyant force experienced by …

Bernoulli’s principle in a spray gun

July 9th, 2022jeefirst0 Comments

JEE Advanced 2014 Paper 2, Questions 13 and 14

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 $20 {\rm~mm}$ and $1 {\rm~mm}$ , respectively. The upper end of the container is open to the atmosphere.

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Q.1…