Question

m1= 1kg m2= 2kg m3= 3kg m4= 4kg. find position of center of man?
​

Answer 1

Given :

Four particles having different masses are arranged as shown in the figure.

To Find :

Position of centre of mass.

Solution :

❖ Centre of mass is an imaginary point where the whole mass of system can be assumed to be concentrated.

A] x - coordinate of COM :

$\sf:\implies\:x_{CM}=\dfrac{m_1x_1+m_2x_2+m_3x_3+m_4x_4}{m_1+m_2+m_3+m_4}$

$\sf:\implies\:x_{CM}=\dfrac{1(0)+2(a)+3(a)+4(0)}{1+2+3+4}$

$\sf:\implies\:x_{CM}=\dfrac{2a+3a}{10}$

$\sf:\implies\:x_{CM}=\dfrac{5a}{10}$

$\sf:\implies\:x_{CM}=\left(\dfrac{a}{2}\right)$

B] y - coordinate of COM :

$\sf:\implies\:y_{CM}=\dfrac{m_1y_1+m_2y_2+m_3y_3+m_4y_4}{m_1+m_2+m_3+m_4}$

$\sf:\implies\:y_{CM}=\dfrac{1(0)+2(0)+3(b)+4(b)}{1+2+3+4}$

$\sf:\implies\:y_{CM}=\dfrac{3b+4b}{10}$

$\bf:\implies\:y_{CM}=\left(\dfrac{7b}{10}\right)$

♦ Position of centre of mass :

$\bigstar\:\underline{\boxed{\bf{\orange{(x_{CM},y_{CM})=\left(\dfrac{a}{2},\dfrac{7b}{10}\right)}}}}$

Answer 2

Given :

Four particles having different masses are arranged as shown in the figure.

To Find :

Position of centre of mass.

Solution :

❖ Centre of mass is an imaginary point where the whole mass of system can be assumed to be concentrated.

A] x - coordinate of COM :

$\sf:\implies\:x_{CM}=\dfrac{m_1x_1+m_2x_2+m_3x_3+m_4x_4}{m_1+m_2+m_3+m_4}$

$\sf:\implies\:x_{CM}=\dfrac{1(0)+2(a)+3(a)+4(0)}{1+2+3+4}$

$\sf:\implies\:x_{CM}=\dfrac{2a+3a}{10}$

$\sf:\implies\:x_{CM}=\dfrac{5a}{10}$

$\sf:\implies\:x_{CM}=\left(\dfrac{a}{2}\right)$

B] y - coordinate of COM :

$\sf:\implies\:y_{CM}=\dfrac{m_1y_1+m_2y_2+m_3y_3+m_4y_4}{m_1+m_2+m_3+m_4}$

$\sf:\implies\:y_{CM}=\dfrac{1(0)+2(0)+3(b)+4(b)}{1+2+3+4}$

$\sf:\implies\:y_{CM}=\dfrac{3b+4b}{10}$

$\bf:\implies\:y_{CM}=\left(\dfrac{7b}{10}\right)$

♦ Position of centre of mass :

$\bigstar\:\underline{\boxed{\bf{\orange{(x_{CM},y_{CM})=\left(\dfrac{a}{2},\dfrac{7b}{10}\right)}}}}$