Three masses are placed on the x-axis: $300 ext{ g}$ at the origin, $500 ext{ g}$ at $x = 40 ext{ cm}$,

Question

Three masses are placed on the x-axis: $300 	ext{ g}$ at the origin, $500 	ext{ g}$ at $x = 40 	ext{ cm}$, and $400 	ext{ g}$ at $x = 70 	ext{ cm}$. The distance of the center of mass from the origin is:

Accepted Answer

The position of the center of mass $X_{cm}$ for a system of particles on the x-axis is given by:
$X_{cm} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3}$
Given:
$m_1 = 300 	ext{ g}$, $x_1 = 0 	ext{ cm}$ (at the origin)
$m_2 = 500 	ext{ g}$, $x_2 = 40 	ext{ cm}$
$m_3 = 400 	ext{ g}$, $x_3 = 70 	ext{ cm}$
Substituting the values:
$X_{cm} = \frac{300(0) + 500(40) + 400(70)}{300 + 500 + 400}$
$X_{cm} = \frac{0 + 20000 + 28000}{1200}$
$X_{cm} = \frac{48000}{1200} = 40 	ext{ cm}$

Step-by-Step Solution

Practice All PHYSICS Questions