Consider the following two statements : (A) Linear momentum of the system remains constant.
Consider the following two statements :
(A) Linear momentum of the system remains constant. (B) Centre of mass of the system remains at rest.
(a) A implies B and B implies A.
(b) A does not imply B and B does not imply A.
(c) A implies B but B does not imply A.
(d) B implies A but A does not imply B.
4 views
1 Answers
(d) B implies A but A does not imply B.
Explanation:
Position of CoM is given by R =(1/M)Σimiri . If we differentiate both sides w.r.t. time t, we get, dR/dt =(1/M)Σimi.dri/dt vcm=(1/M)Σimivi Now if
(B) is true, it means vcm = 0,
→ Σimivi = 0 =Constant.
So (B) implies (A).
Now let us check if (A) is true but not equal to zero
→ Σimivi = k Then vcm=(1/M)k =k/M =not equal to zero. i.e. CoM of the system is not at rest. So (A) does not imply (B).
4 views
Answered