Question

3. The center of mass (or center of gravity) of a two-particle system is at the origin. One particle

is located at (3.0 m, 0.0 m) and has a mass of 2.0 kg. The other particle has a mass of 3.0 kg.
What is the location of the 3.0-kg particle?
A) (-3.0 m, 0.0 m)
B) (-2.0 m, 0.0 m)
C) (2.0 m, 0.0 m)
D) (3.0 m, 0.0 m)

Answer 1

B) (-2.0 m, 0.0 m)

Step-by-step explanation:

Given:

Mass of particle 1 is,
`m_1=2.0\ kg`

Mass of particle 2 is,
`m_2=3.0\ kg`

Position of center of mass is,
`(x_(cm),y_(cm))=(0,0)`

Position of particle 1 is,
`(x_1,y_1)=(3.0\ m,0.0\ m)`

Position of particle 2 is,
`(x_2,y_2)=(?\ m,?\ m)`

We know that, the x-coordinate of center of mass of two particles is given as:

`x_(cm)=(m_1x_1+m_2x_2)/(m_1+m_2)`

Plug in the values given.

`0=((2.0* 3)+(3.0* x_2))/(2.0+3.0)\\\\0=6+3x_2\\\\3x_2=-6\\\\x_2=(-6)/(3)=-2.0\ m`

We know that, the y-coordinate of center of mass of two particles is given as:

`y_(cm)=(m_1y_1+m_2y_2)/(m_1+m_2)`

Plug in the values given.

`0=((2.0* 0)+(3.0* y_2))/(2.0+3.0)\\\\0=0+3y_2\\\\3y_2=0\\\\y_2=(0)/(3)=0.0\ m`

Therefore, the position of particle 2 of mass 3.0 kg is (-2.0 m, 0.0 m).

So, option (B) is correct.