Question

Two bodies of masses 1 kg and 2 kg are lying in xy plane at (-1,2) and (2,4) respectively.
What are the coordinate of the centre of mass?​

Answer 1

GivEn:

• Two bodies of masses 1 kg and 2 kg are lying in xy plane at (-1,2) and (2,4) respectively.

To find:

• Coordinate of the centre of mass

SoluTion:

$\underline{\bigstar\:\boldsymbol{As\;per\:givEn\:QuesTion\::}}$

$\;\;\;\bullet\;\sf Mass\;of\;1st\;body,\; ( m_1 )\;:\; \bf{1\;kg}\\\\ \;\;\;\bullet\;\sf Mass\;of\;2nd\;body,\; ( m_2 )\;:\; \bf{2\;kg}\\\\ \;\;\;\bullet\;\sf Let\;the\; coordinates\;of\;the\;centre\;of\;mass\;be\;(x , y)$

$\rule{150}{2}$

$\maltese\;{\boxed{\sf{x = \dfrac{ m_1 x_1 + m_2 x_2 }{ m_1 + m_2 }}}}\\\\ :\implies\sf \dfrac{ 1 \times (- 1) + 2 \times 2}{1 + 2}\\\\ :\implies\sf \dfrac{-1 + 4}{3}\\\\ :\implies{\underline{\boxed{\sf{\pink{1}}}}}\;\bigstar$

Now,

$\maltese\;{\boxed{\sf{y = \dfrac{ m_1 y_1 + m_2 y_2 }{ m_1 + m_2 }}}}\\\\ :\implies\sf \dfrac{ 1 \times 2 + 2 \times 4}{1 + 2}\\\\ :\implies\sf \dfrac{2 + 8}{3}\\\\ :\implies{\underline{\boxed{\sf{\purple{ \dfrac{10}{3}}}}}}\;\bigstar\\\\ \therefore\;\sf The\; coordinates\;of\;centre\;of\;mass\;be\; \bigg(1, \dfrac{10}{3} \bigg).$

Answer 2

Answer:

1,10/3

Explanation:

Basically centre of mass of any points in the space can be given by

X= m1x1+m2x2/m1+m2

Therefore X coordinate of centre of mass = 1*-1 + 2*2/3= 3/3 = 1

Similarly Y coordinate = 1*2+2*4/3= 10/3

Therefore coordinates are  (1,10/3)