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Chapter 12: Q. 7 (page 330)

The three masses shown in FIGURE EX12.7 are connected by massless, rigid rods. What are the coordinates of the center of mass?

Short Answer

Expert verified

The coordinates of the center of mass are $(8 cm, 5 cm)$

Step by step solution

01

Step 1. Given information

Let us assume that the mass $300 g$ be at origin.

The co-ordinates of ball A $200 g$ is $(0, 0)$

The co-ordinates of ball B $300 g$ is $(12 cm, 10 cm)$

The co-ordinates of ball C $100 g$ is $(12 cm, 0)$

02

Step 2. Explanation

The x - xoordinate of center of mass is

$\begin{array}{l} x_{c m} = \frac{m_{A} x_{A} + m_{B} x_{B} + m_{C} x_{C}}{m_{A} + m_{B} + m_{C}} \\ x_{cm} = \frac{(200 g) (0 cm) + (300 g) (12 cm) + (100 g) (12 cm)}{(200 g) + (300 g) + (100 g)} \\ x_{cm} = 8 cm \end{array}$

The y- coordinate of center of mass is

$\begin{array}{l} y_{c m} = \frac{m_{A} y_{A} + m_{B} y_{B} + m_{C} y_{C}}{m_{A} + m_{B} + m_{C}} \\ y_{cm} = \frac{(200 g) (0 cm) + (300 g) (10 cm) + (100 g) (0 cm)}{(200 g) + (300 g) + (100 g)} \\ y_{cm} = 5 cm \end{array}$

Therefore, the coordinates of the center of mass are $(8 cm, 5 cm)$

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