Two particles of masses 2 kg and 4 kg are approaching each other with acceleration `1 ms^(-2)` and `2 ms^(-2)`, respectively, on a smooth horizontal surface. Find the magnitude of acceleration of center of mass of the system.

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

A

Explanation

The acceleration of center of mass of the system
`a_(CM) = |m_(1)a_(2) + m_(2)a_(2)|/(m_(1) + m_(2))`
`rArr a_(CM) = |m_(1)a_(2) + m_(2)a_(2)|/(m_(1) + m_(2))`
`=(2xx 1-4xx2)/(2+4) = -1 ms^(2)`
[-ve sign because direction of 4 kg is opposite to that of 2kg]
Since `m_(2)a_(2) gt m_(1)a_(1)` so the direction of acceleration of center of mass will be directed towards `a_(1)`