# Consider the Following Two Statements: (A) Linear Momentum of the System Remains Constant. (B) Centre of Mass of the System Remains at Rest. - Physics

MCQ

Consider the following two statements:

(A) Linear momentum of the system remains constant.

(B) Centre of mass of the system remains at rest.

#### Options

• A implies B and B implies A.

• A does not imply B and B does not imply A.

• A implies B but B does not imply A.

• B implies A but A does not imply B.

#### Solution

B implies A but A does not imply B.

The centre of mass of a system is given by,
$\vec{R} = \frac{1}{M} \sum_{} m_i \vec{r}_i$
On differentiating the above equation with respect to time, we get:
$\frac{d \vec{R}}{dt} = \frac{1}{M} \sum_{} m_i \frac{d \vec{r}_i}{d t}$

As the centre of mass of the system remains at rest, we have:
$\frac{1}{M} \sum_{} m_i \frac{d \vec{r}_i}{d t} = 0$
$\sum_{} m_i \vec{v}_i = 0$
This implies that the linear momentum of the system remains constant.

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 2 | Page 157