The centre of mass of a system of two particles of masses m1 and m2 is at a distance d1from m1 and at a distance d2 from mass m2 such that

Question

The centre of mass of a system of two particles of masses m1 and m2 is at a distance d1from m1 and at a distance d2 from mass m2 such that (A) (d1/d2) = (m2/m1) (B) (d1/d2) = (m1/m2) (C) (d1/d2) = (m1/m1+m2) (D) (d1/d2) = (m2/m1+m2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/172e32de523697ed0fcab668ab766887-.png" /> Refer figure. The distances of centre of mass CM from masses m1 and m2 are d1 = (m2d/m1+m2) and d2 = (m1d/m1 +m2) ∴ (d1/d2) = (m2/m1)

Q. The centre of mass of a system of two particles of masses $m_{1}$ and $m_{2}$ is at a distance $d_{1}$ from $m_{1}$ and at a distance $d_{2}$ from mass $m_{2}$ such that

$\frac{d _{1}}{d _{2}} = \frac{m _{2}}{m _{1}}$

$\frac{d _{1}}{d _{2}} = \frac{m _{1}}{m _{2}}$

$\frac{d _{1}}{d _{2}} = \frac{m _{1}}{m _{1} + m _{2}}$

$\frac{d _{1}}{d _{2}} = \frac{m _{2}}{m _{1} + m _{2}}$

Refer figure. The distances of centre of mass $CM$ from masses $m_{1}$ and $m_{2}$ are
$d_{1} = \frac{m _{2} d}{m _{1} + m _{2}}$ and
$d_{2} = \frac{m _{1} d}{m _{1} + m _{2}}$
$∴ \frac{d _{1}}{d _{2}} = \frac{m _{2}}{m _{1}}$

Q. The centre of mass of a system of two particles of masses m1​ and m2​ is at a distance d1​from m1​ and at a distance d2​ from mass m2​ such that

d2​d1​​=m1​m2​​

d2​d1​​=m2​m1​​

d2​d1​​=m1​+m2​m1​​

d2​d1​​=m1​+m2​m2​​