Advertisement Remove all ads

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


Consider the following two statements:

(A) Linear momentum of the system remains constant.

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


  • 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. 

Advertisement Remove all ads


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?
Advertisement Remove all ads


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

View all notifications

      Forgot password?
View in app×