First slide

Location of centre on mass for multiple point masses

Question

Three particles of masses 1 kg, 2kg and 3kg are situated at the corners of an equilateral triangle of side b. The coordinates of the centre of mass are (x -axis along line joining 1kg and 2kg with origin at 1 kg mass)

Moderate

A

$[0, \frac{7 b}{12}, \frac{3 \sqrt{3} b}{12}]$
B

$[\frac{3 \sqrt{3} b}{12}, \frac{7 b}{12}, 0]$
C

$[\frac{7 b}{12}, \frac{3 \sqrt{3} b}{12}, 0]$
D

$[\frac{7 b}{12}, 0, \frac{3 \sqrt{3} b}{12}]$

Solution

$c o o r d i n a t i n g o f 3 k g = (\frac{b}{2}, \frac{\sqrt{3} b}{2})$
$x_{c m} = \frac{1 \times 0 + 2 b + 3 \times \frac{b}{2}}{6} = \frac{7 b}{12}$ $, y_{c m} = \frac{1 \times 0 + 2 \times 0 + 3 \times \frac{\sqrt{3}}{2} b}{6} = \frac{3 \sqrt{3} b}{12}$
$z_{c m} = \frac{1 \times 0 + 2 \times 0 + 3 \times 0}{6} = 0$
$C o o r d i n a t e s o f t h e c e n t e r o f m a s = (\frac{7 b}{12}, \frac{3 \sqrt{3} b}{12}, 0)$

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