(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 a¯ with respect to the centre of the polygon. Find the position vector of centre of mass

(n−1)mr+ma(n−1)m+m=0⇒ (n−1)mr+ma=0⇒r=−a(n−1)Negative sign indicates that r →is in a direction opposite to a¯.r→=−a→(n−1)

(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 a¯ with respect to the centre of the polygon. Find the position vector of centre of mass

(n−1)mr+ma(n−1)m+m=0⇒ (n−1)mr+ma=0⇒r=−a(n−1)Negative sign indicates that r →is in a direction opposite to a¯.r→=−a→(n−1)

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(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 $\bar{a}$ with respect to the centre of the polygon. Find the position vector of centre of mass

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$\bar{r} = - \frac{\bar{a} (n)}{(n - 1)}$

$\bar{r} = \frac{- \bar{a}}{(n - 1)}$

$\bar{r} = - \frac{\bar{a}}{n}$

$\bar{r} = - \bar{a}$

answer is B.

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Detailed Solution

$\frac{(n - 1) m r + m a}{(n - 1) m + m} = 0$

$\Rightarrow (n - 1) m r + m a = 0$

$\Rightarrow r = \frac{- a}{(n - 1)}$

$Negative sign indicates that \vec{r} is in a direction opposite to \bar{a} .$

$\vec{r} = - \frac{\vec{a}}{(n - 1)}$

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(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 a¯ with respect to the centre of the polygon. Find the position vector of centre of mass

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(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 $\bar{a}$ with respect to the centre of the polygon. Find the position vector of centre of mass