A small spherical ball of… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

2022integerhard

A small spherical ball of radius $0.1\mathrm{mm}$ and density ${10}^{4}\mathrm{kg}{m}^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $h$ will be ____ $m$ . (Given $g=10{ms}^{-2}$ , viscosity of water $=1.0\times {10}^{-5}N‐s{m}^{-2}$ ).

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Held on 29 Jun 2022 · Verified 6 Jul 2026.

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Solution

JEE Main 2022 Physics, Mechanical Properties of Fluids — solution figure

Using equation of motion, ${v}^{2}={u}^{2}+2as$

${v}^{2}=0+2(-g)(-h)$

$\Rightarrow {v}^{2}=2gh$

Initial velocity of ball is $v=\sqrt{2gh}=\sqrt{20h}$ .

If after entering the water this velocity does not change, then this value should be equal to the terminal velocity.

Then, $\sqrt{2gh}=\frac{2}{9}\frac{{r}^{2}(\rho -\sigma )g}{\eta }$ , here, $\rho$ is density of ball, $\sigma$ is density of water and $\eta$ is viscosity.

$\Rightarrow \sqrt{20h}=\frac{2}{9}\frac{{(0.1\times {10}^{-3})}^{2}({10}^{4}-{10}^{3})10}{1\times {10}^{-5}} \Rightarrow \sqrt{20h}=\frac{2}{9}\frac{{10}^{-8}(10-1){10}^{3}\times 10}{1\times {10}^{-5}}$

$\Rightarrow 20h=400$

$\therefore h=20m$

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Solution

JEE Main 2022 Physics, Mechanical Properties of Fluids — solution figure

Using equation of motion, ${v}^{2}={u}^{2}+2as$

${v}^{2}=0+2(-g)(-h)$

$\Rightarrow {v}^{2}=2gh$

Initial velocity of ball is $v=\sqrt{2gh}=\sqrt{20h}$ .

If after entering the water this velocity does not change, then this value should be equal to the terminal velocity.

Then, $\sqrt{2gh}=\frac{2}{9}\frac{{r}^{2}(\rho -\sigma )g}{\eta }$ , here, $\rho$ is density of ball, $\sigma$ is density of water and $\eta$ is viscosity.

$\Rightarrow 20h=400$

$\therefore h=20m$

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Solution

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JEE Main Mechanics in other years

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Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics