Question

a system having two ideal particle the particle is at rest and me other particle is at having an acceleration a the acceleration of com is​

Answer 1

The acceleration of the center of mass of a system of two particles of masses $\sf{m_1}$ and $\sf{m_2}$ having accelerations $\bf{a_1}$ and $\bf{a_2}$ respectively is given by,

$\longrightarrow\bf{\bar a}=\dfrac{\sf{m_1}\bf{a_1}+\sf{m_2}\bf{a_2}}{\sf{m_1+m_2}}$

According to the question, the two particles are ideal so their masses are same.

• $\sf{m_1=m_2=m}$

Here first particle is at rest so it has no acceleration.

• $\bf{a_1}=\sf{0}$

And the second particle moves with acceleration,

• $\bf{a_2}=\sf{a}$

Hence the acceleration of the center of mass is,

$\longrightarrow\bf{\bar a}=\dfrac{\sf{m}(0)+\sf{ma}}{\sf{m+m}}$

$\longrightarrow\bf{\bar a}=\dfrac{\sf{ma}}{\sf{2m}}$

$\longrightarrow\underline{\underline{\bf{\bar a}=\dfrac{\sf{a}}{\sf{2}}}}$