Three particles having masses 1, 2, and 3 kg are located on the x-axis at -1,2,3 respectively. The center of mass of this system is located at x =

A) $\frac { 1,125 } { 8 }$
B) $\frac { 500 } { 3 }$
C)2
D) $\frac { 15,625 } { 24 }$
E) $\frac { 125 } { 24 }$

Question

Three particles having masses 1, 2, and 3 kg are located on the x-axis at -1,2,3 respectively. The center of mass of this system is located at x =

A) $\frac { 1,125 } { 8 }$
B) $\frac { 500 } { 3 }$
C)2
D) $\frac { 15,625 } { 24 }$
E) $\frac { 125 } { 24 }$

Quizplus · Accepted Answer

The center of mass $ x_{cm} $ is calculated using the formula: $ x_{cm} = \frac{\sum m_ix_i}{\sum m_i} $. Here, $ m_1 = 1 \, \text{kg}, x_1 = -1 $, $ m_2 = 2 \, \text{kg}, x_2 = 2 $, $ m_3 = 3 \, \text{kg}, x_3 = 3 $. Thus, $ x_{cm} = \frac{(1 \times -1) + (2 \times 2) + (3 \times 3)}{1 + 2 + 3} = \frac{-1 + 4 + 9}{6} = \frac{12}{6} = 2 $.

Three Particles Having Masses 1, 2, and 3 Kg Are 1,1258\frac { 1,125 } { 8 }81,125​

Three Particles Having Masses 1, 2, and 3 Kg Are $\frac { 1,125 } { 8 }$