What is the position vector of centre of...

What is the position vector of centre of mass of two particles of equal masses ?

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To find the position vector of the center of mass (COM) of two particles with equal masses, we can follow these steps: ### Step-by-Step Solution: 1. **Define the Masses and Position Vectors**: Let the two particles have equal masses, denoted as \( m_1 = m_2 = m \). Let their position vectors be \( \vec{R_1} \) and \( \vec{R_2} \). 2. **Write the Formula for Center of Mass**: ...

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The centre of mass of two particles system lies

at the midpoint on the line joining the two particles.

at one end of line joining the two particles

on the line perpendicular to the line joining two particles

on the line joining the two particles

If vec(R)_(CM) is the position of the centre of mass of a system of two particles of masses m_(1) and m_(2) then vec(R)_(CM) is given by :

`(m_(1)+m_(2))/(m_(1)vec(r)_(1)+m_(2)vecr_(2))`

`(m_(1)m_(2))/(m_(1)vec(r)_(1)+m_(2)vec(r)_(2))`

` (m_(1)vec(r)_(1)+m_(2)vec(r)_(2))/(m_(1)+m_(2))`

`(m_(1)vec(r)_(1)+m_(2)vec(r)_(2))/(m_(1)m_(2))`

What will be the position of centre of mass of a half disc shown ? .

`(2 a)/(pi)`

`(4 a)/(3 pi)`

`(a)/(pi)`

`(2 a)/(3 pi)`