Three identical spheres each of… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

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Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $3m$ each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt{x}m$ . The value of $x$ is

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Held on 25 Jul 2022 · Verified 6 Jul 2026.

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Solution

JEE Main 2022 Physics, Center of Mass Momentum and Collision — solution figure

The diagram represents the locations of the masses as mentioned in the question.

For point $1$ , $\vec{{r}_{1}}=0\hat{i}+0\hat{j}$ for point $2$ , $\vec{{r}_{2}}=3\hat{i}+0\hat{j}$ and for point $3$ , $\vec{{r}_{3}}=0\hat{i}+3\hat{j}$ .

The formula for centre of mass is

${\vec{r}}_{com}=\frac{{m}_{1}\vec{{r}_{1}}+{m}_{2}\vec{{r}_{2}}+{m}_{3}\vec{{r}_{3}}}{{m}_{1}+{m}_{2}+{m}_{3}}$

$\Rightarrow {\vec{r}}_{\mathrm{com}}=\frac{M(0\hat{i}+0\hat{j})+M(3\hat{i})+M(3\hat{j})}{3M}$

$\Rightarrow {\vec{r}}_{\mathrm{com}}=\hat{i}+\hat{j}$

$|{\vec{r}}_{\mathrm{com}}|=\sqrt{{1}^{2}+{1}^{2}}=\sqrt{2}=\sqrt{x}$

$\Rightarrow x=2$

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Solution

JEE Main 2022 Physics, Center of Mass Momentum and Collision — solution figure

The diagram represents the locations of the masses as mentioned in the question.

For point $1$ , $\vec{{r}_{1}}=0\hat{i}+0\hat{j}$ for point $2$ , $\vec{{r}_{2}}=3\hat{i}+0\hat{j}$ and for point $3$ , $\vec{{r}_{3}}=0\hat{i}+3\hat{j}$ .

The formula for centre of mass is

${\vec{r}}_{com}=\frac{{m}_{1}\vec{{r}_{1}}+{m}_{2}\vec{{r}_{2}}+{m}_{3}\vec{{r}_{3}}}{{m}_{1}+{m}_{2}+{m}_{3}}$

$\Rightarrow {\vec{r}}_{\mathrm{com}}=\frac{M(0\hat{i}+0\hat{j})+M(3\hat{i})+M(3\hat{j})}{3M}$

$\Rightarrow {\vec{r}}_{\mathrm{com}}=\hat{i}+\hat{j}$

$|{\vec{r}}_{\mathrm{com}}|=\sqrt{{1}^{2}+{1}^{2}}=\sqrt{2}=\sqrt{x}$

$\Rightarrow x=2$

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Solution

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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