Question

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The centre of mass has an acceleration
(a) zero
(b) 12→a
(c) →a
(d) 2→a

Answer 1

The center of mass has an acceleration of two identical particles with one at rest and other has an acceleration is $\frac{a}{2}$ or  $\frac{1}{2} -> a$

Explanation:

Acceleration of mass center given by the following

Let $a_(cm)$ be the acceleration of the center of mass of the two particles. Then,

$\text {acceleration of the center of mass}=\frac{\left(m \times a_{1}\right)+\left(m \times a_{2}\right)}{m+m}$

$\text {acceleration of the center of mass}=\frac{(m \times a)+(m \times 0)}{2 m}$

$\text {acceleration of the center of mass}=\frac{m a}{2 m}$

Description of each mass to accelerate,

By total mass. so, we get

Hence,  $\text {acceleration ofthe center of mass}=\frac{a}{2}$

The center of mass has an acceleration of $\frac{a}{2}$ or $\frac{1}{2} -> a$

The same formula is used to calculate both velocity and origin position.  

Answer 2

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The centre of mass has accelaration a/2