Ncert Exercises & Solutions

Q. 22 (n — 1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector with respect to the center of the polygon. Find the position vector of the center of mass.

Hint:

\sum_{i} m_{i} \vec{r_{i}}

is zero at the center of mass.

Step 1: Find the position vector of the center of mass By equating

\sum_{i} m_{i} \vec{r_{i}} = 0 .

Let x be the distance of center of mass.

Now,

(n - 1) m x + m a = 0

(n - 1) m x = - m a

x = - ( n - 1 ) a

The center of mass will get shifted in the opposite direction with reference to the position vector of the vacant vertex.

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