Question

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration “a”. The center of mass has an acceleration.

• A. a
• B. $2\mathrm{a}$
• C. $\frac{1}{2}\mathrm{a}$
• D. Zero

Answer 1

The correct option is C

$\frac{1}{2}\mathrm{a}$

Step 1: Given information

According to the question,

${\mathrm{m}}_1={\mathrm{m}}_2=\mathrm{m}$

$$\begin{gathered} {\mathrm{a}}_1=0 \\ {\mathrm{a}}_2=\mathrm{a} \end{gathered}$$

Here,

m is the mass.

a is the acceleration.

Step 2: To find

We have to determine the acceleration of the center of mass of a two particles system.

Step 3: Calculation

The formula for acceleration for the center of mass is:

${\overrightarrow{\mathrm{a}}}_{\mathrm{cm}}=\frac{{\mathrm{m}}_1\overrightarrow{{\mathrm{a}}_1}+{\mathrm{m}}_2\overrightarrow{{\mathrm{a}}_2}}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

Here,

${\mathrm{m}}_1={\mathrm{m}}_2=\mathrm{m}=\mathrm{mass}$

${\mathrm{a}}_1={\mathrm{a}}_2=\mathrm{acceleration}$

By substituting the values, we get

$$\begin{gathered} \overrightarrow{{\mathrm{a}}_{\mathrm{cm}}}=\frac{\mathrm{m}\times 0+\mathrm{m}\overrightarrow{\mathrm{a}}}{2\mathrm{m}} \\ =\frac{1}{2}\overrightarrow{\mathrm{a}} \end{gathered}$$

Therefore, option C is the correct answer.