First slide

Location of centre on mass for multiple point masses

Question

Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side $ℓ$ .The (X)
coordinate of center of mass is

Moderate

A

$\frac{7}{12} ℓ$
B

$\frac{5}{9} ℓ$
C

$\frac{7 \sqrt{2}}{9} ℓ$
D

$\frac{\sqrt{5}}{9} ℓ$

Solution

$X_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}} = \frac{2 \times 0 + 3 \times ℓ + 4 \times \frac{ℓ}{2}}{2 + 3 + 4} = \frac{5}{9} ℓ$

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