Statement-1 : The centre of mass of a two particle system lies on the line joining the two particles, being closer to the heavier particle.
Statement-2 : Product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.

Options

A. If both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If assertion is true but reason is false.
D. If the assertion and reason both are false.

Answer

A

Explanation

If centre of mass of system lies at origin then `vec(r)_(cm)= 0`

`vec(r)_(cm)= (m_(1) vec(r)_(1) + m_(2) vec(r)_(2))/(m_(1) + m_(2))`
`therefore m_(1) vec(r)_(1) + m_(2) vec(r)_(2) = 0 or m_(1) r_(1)= m_(2) r_(2)`
It is clear that if `m_(1) gt m_(2) " then " r_(1) lt r_(2)`