A particle of mass m is dropped… - JEE Main 2020 Physics PYQ

JEE Main 2020 — Physics Mechanics

2020mcqhard

A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}.$ If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is:

Official previous-year question

Held on 8 Jan 2020 · Verified 6 Jul 2026.

Options

A
$\sqrt{\frac{1}{2}}$
B
$\sqrt{\frac{3}{4}}$
C
$\frac{1}{2}$
D
$\sqrt{\frac{3}{2}}$

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Solution

time for collision ${t}_{1}=\frac{h}{\sqrt{2gh}}$

After ${t}_{1}$

${V}_{A}=0-g{t}_{1}=-\sqrt{\frac{gh}{2}}$

and ${V}_{B}=\sqrt{2gh}-g{t}_{1}=\sqrt{gh}[\sqrt{2}-\frac{1}{\sqrt{2}}]$

at the time of collision

${\vec{p}}_{i}=\vec{{p}_{f}}$

$\Rightarrow m{\vec{V}}_{A}+m{\vec{V}}_{B}=2m{\vec{V}}_{f}$

$\Rightarrow -\sqrt{\frac{gh}{2}}+\sqrt{gh}[\sqrt{2}-\frac{1}{\sqrt{2}}]=2{\vec{V}}_{f}$

${V}_{f}=0$

and height from ground

$=h-\frac{1}{2}g{t}_{1}^{2}=h-\frac{h}{4}=\frac{3h}{4}$

so time ,

$t=\sqrt{2\times \frac{(\frac{3h}{4})}{g}}=\sqrt{\frac{3}{2}}\sqrt{\frac{h}{g}}$

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Solution

time for collision ${t}_{1}=\frac{h}{\sqrt{2gh}}$

After ${t}_{1}$

${V}_{A}=0-g{t}_{1}=-\sqrt{\frac{gh}{2}}$

and ${V}_{B}=\sqrt{2gh}-g{t}_{1}=\sqrt{gh}[\sqrt{2}-\frac{1}{\sqrt{2}}]$

at the time of collision

${\vec{p}}_{i}=\vec{{p}_{f}}$

$\Rightarrow m{\vec{V}}_{A}+m{\vec{V}}_{B}=2m{\vec{V}}_{f}$

$\Rightarrow -\sqrt{\frac{gh}{2}}+\sqrt{gh}[\sqrt{2}-\frac{1}{\sqrt{2}}]=2{\vec{V}}_{f}$

${V}_{f}=0$

and height from ground

$=h-\frac{1}{2}g{t}_{1}^{2}=h-\frac{h}{4}=\frac{3h}{4}$

so time ,

$t=\sqrt{2\times \frac{(\frac{3h}{4})}{g}}=\sqrt{\frac{3}{2}}\sqrt{\frac{h}{g}}$

Options

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Solution

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Options

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