First slide

Location of centre on mass for multiple point masses

Question

Three identical spheres, each of mass M, are placed at the comers of a right angle triangle with the mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass. [NEET 2020]

Moderate

A

$2 (\hat{i} + \hat{j})$
B

$(\hat{i} + \hat{j})$
C

$\frac{2}{3} (\hat{i} + \hat{j})$
D

$\frac{4}{3} (\hat{i} + \hat{j})$

Solution

The given situation as shown in the figure.
$OA = 2 \hat{i}$
$OB = 2 \hat{j}$
Position vector of centre of mass,
$R_{CM} = \frac{M_{1} r_{1} + M_{2} r_{2} + M_{3} r_{3}}{M_{1} + M_{2} + M_{3}} = \frac{M (OA) + M (OB)}{M + M + M}$
$= \frac{M \times 2 \hat{i} + M \times 2 \hat{j}}{3 M} = \frac{2}{3} (\hat{i} + \hat{j})$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App