Question

Choose the correct statement,
A.The position of centre of mass of a system is dependent on the choice of coordinate system.
B.Newton’s second law of motion is applicable to the centre of mass of the system.
C.When no external force acts on a body, the acceleration of centre of mass is zero.
D.Internal forces can change the state of the centre of mass.

A.Both A) and B) are correct.
B.Both B) and C) are wrong.
C.Both A) and C) are wrong.
D.Both A) and D) are wrong.

Answer 1

Hint: Acceleration of centre of mass is directly proportional to the external force applied on the body. This information will help you to get the required solution.

Formula used:
Acceleration of centre of mass is given by,
     \[{{a}_{cm}}=\dfrac{{{F}_{ext}}}{m}\]
where, \[{{F}_{ext}}\] is the external force acting on a body and m is mass of the body.

Complete step by step answer:
A. The mass distribution of the body determines the position of centre of mass. Therefore, the centre of mass is independent of the coordinate system. Hence, statement A is incorrect.
B. According to Newton’s second law, acceleration is directly proportional to the external force acting on the system. Since, acceleration of centre of mass is given by, \[{{a}_{cm}}=\dfrac{{{F}_{ext}}}{m}\], it can be said that Newton’s second law of motion is applicable to the centre of mass. Hence, statement B is correct.
C. Since, acceleration due to centre of mass is given by \[{{a}_{cm}}=\dfrac{{{F}_{ext}}}{m}\], it is obvious that when \[{{F}_{ext}}\] is zero, that is, no external force acts on the body, acceleration due to centre of mass will also be zero. Hence, statement C is correct.
D. Acceleration due to centre of mass depends upon the external force acting on a system and not internal force. Therefore, internal forces cannot affect the centre of mass. Hence statement D is correct.

So, the correct answer is “Option D”.

Note: The formula for acceleration due to centre of mass is vital for answering this question. Also, it should be kept in mind that stating F as \[{{F}_{ext}}\]in the formula is important.