Question

Three point particles of mass $1kg,1.5kgand2.5kg$ are placed at three corners of a right triangle of sides $4.0cm,3.0cmand5.0cm$ as shown in the figure. The centre of mass of the system is at the point:

• A. $0.9cm$ right and $2.0cm$ above $1kg$mass
• B. $2.0cm$ right and $0.9cm$ above $1kg$ mass
• C. $1.5cm$ right and $1.2cm$ above $1kg$ mass
• D. $0.6cm$right and $2.0cm$ above $1kg$mass

Answer 1

The correct option is A

$0.9cm$ right and $2.0cm$ above $1kg$mass

Step 1: Given information

1. Three-point particles of mass $1kg,1.5kgand2.5kg$
2. Three corners of a right triangle of sides $4.0cm,3.0cmand5.0cm$

Step 2: Draw a diagram

Step 3: Explanation

Taking $1kg$ as the origin,

For $x-axis$,

$x_{com}=\frac{(m_1{x}_1+m_2{x}_2+m_3{x}_3)}{(m_1+m_2+m_3)}$

$x_{com}=\frac{(1\times 0+1.5\times 3+2.5\times 0)}{5}$

$x_{com}=0.9$

For $y-axis$,

$y_{com}=\frac{(m_1{y}_1+m_2{y}_2+m_3{y}_3)}{(m_1+m_2+m_3)}$

$y_{com}=\frac{(1\times 0+1.5\times 0+2.5\times 4)}{5}$

$y_{com}=2$

The center of mass is at $(0.9,2)$.

Hence, the correct option is (A).