Respuesta :
Answer:
center of mass of the two masses will lie at x = 2.52 cm
center of gravity of the two masses will lie at x = 2.52 cm
So center of mass is same as center of gravity because value of gravity is constant here
Explanation:
Position of centre of mass is given as
[tex]r_{cm} = \frac{m_1r_1 + m_2r_2}{m_1 + m_2}[/tex]
here we have
[tex]m_1 = 10.2 kg[/tex]
[tex]m_2 = 4.6 kg[/tex]
[tex]r_1 = (0, 0)[/tex]
[tex]r_2 = (8.1cm, 0)[/tex]
now we have
[tex]r_{cm} = \frac{10.2 (0,0) + 4.6 (8.1 , 0)}{10.2 + 4.6}[/tex]
[tex]r_{cm} = {(37.26, 0)}{14.8}[/tex]
[tex]r_{cm} = (2.52 cm, 0)[/tex]
so center of mass of the two masses will lie at x = 2.52 cm
now for center of gravity we can use
[tex]r_g_{cm} = \frac{m_1gr_1 + m_2gr_2}{m_1g + m_2g}[/tex]
here we have
[tex]m_1 = 10.2 kg[/tex]
[tex]m_2 = 4.6 kg[/tex]
[tex]r_1 = (0, 0)[/tex]
[tex]r_2 = (8.1cm, 0)[/tex]
now we have
[tex]r_g_{cm} = \frac{10.2(9.8) (0,0) + 4.6(9.8) (8.1 , 0)}{10.2(9.8) + 4.6(9.8)}[/tex]
[tex]r_g_{cm} = {(37.26, 0)}{14.8}[/tex]
[tex]r_g_{cm} = (2.52 cm, 0)[/tex]
So center of mass is same as center of gravity because value of gravity is constant here
