There are two particles of same mass. If one of the particles is at rest always and the other has an acceleration $¯ a$ . Acceleration of center of mass is :

zero

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\frac{1}{2} ¯ a

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¯ a

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centre of mass for such a system can not be defined.

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Solution

The correct option is B $\frac{1}{2} ¯ a$
$a_{c . o . m}$ = $\frac{m_{1} \times a_{1} + m_{2} \times a_{2}}{m_{1} + m_{2}}$
given both body having same mass so
$a_{c . o . m}$ = $\frac{m \times a_{1} + m \times a_{2}}{2 m}$
$a_{1}$ =0 given that body 1 is in rest
so ${¯ a}_{c . o . m}$ = $\frac{1}{2}$ $\times ¯ a$

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