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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassCalculate of COMMedium2 minPYQ_2024

PhysicsMediuminteger

The identical spheres each of mass $2 M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 m$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$ , where the value of $x$ is ________.

Answer:

Solution:

Position vector ${\vec{r}}_{COM} = \frac{m_{1} {\vec{r}}_{1} + m_{2} {\vec{r}}_{2} + m_{3} {\vec{r}}_{3}}{m_{1} + m_{2} + m_{3}}$

${\vec{r}}_{COM} = \frac{2 M \times 0 + 2 M \times 4 \hat{i} + 2 M \times 4 \hat{j}}{6 M}$

$\Rightarrow \vec{r} = \frac{4}{3} \hat{i} + \frac{4}{3} \hat{j}$

$| \vec{r} | = \sqrt{{(\frac{4}{3})}^{2} + {(\frac{4}{3})}^{2}} = \frac{4 \sqrt{2}}{3}$

Therefore, $x = 3$ .

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Calculate of COM

⏱ 2mℹ️ Source: PYQ_2024

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