First slide

Location of centre on mass for multiple point masses

Question

Find out coordinates of centre of mass of the system:

Moderate

A

$(L, \frac{8 L}{5})$
B

$(\frac{34 L}{3}, \frac{4 L}{3})$
C

$(L, \frac{5 L}{8})$
D

$(7 L, \frac{3 L}{2})$

Solution

The coordinates of the particles are given by, m(0, 0), m(2 L, 0), m(2 L, 2 L), m(0.2 L), m(L, 4 L)
$x_{cm} = \frac{(m \times 2 L) + (m \times 2 L) + (m \times L)}{5 m} = L,$
$y_{cm} = \frac{(m \times 2 L) + (m \times 2 L) + (m \times 4 L)}{5 m} = \frac{8 L}{5}$

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