Examine the following two equations:
(A) $\vec{R} = \dfrac{1}{M}\sum_{i} m_i \vec{r}_i$
(B) $\vec{a}_{CM} = \dfrac{\vec{F}}{M}$
In a noninertial reference frame,

Question

Examine the following two equations: (A) R = (1)/(M)∑_ i m_i r _i (B) a _ CM = F M In a noninertial reference frame,

Quantrex Academy · Accepted Answer

Correct answer: B. equation A is correct but B is incorrect

Equation (A) represents the definition of the position vector of the center of mass. It is a purely geometric relation and remains valid in all reference frames, whether inertial or non-inertial.

Equation (B) represents Newton's second law for a system of particles. In a non-inertial reference frame, pseudo forces must be taken into account along with the real external forces. The correct equation in a non-inertial frame is

M\vec{a}_{CM} = \vec{F}_{ext} + \vec{F}_{pseudo}

. Thus, equation (B) is incorrect in a non-inertial frame.

Therefore, equation A is correct but B is incorrect.

Examine the following two equations: (A) R = (1)/(M)∑_ i m_i r _i...

Options

Correct answer

Step-by-step solution

More from Centre of Mass, Linear momentum, Collision