Three particles, each of mass m, are placed at the corner of right angle triangle as shown in the figure. if OA=a and OB=b, the position vector of the centre of mass is :
(here $^i$ and $^j$ are unit vector along x and y axes, respectively )

\frac{1}{3} (a^i + b^j)

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\frac{1}{3} (a^i - b^j)

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\frac{2}{3} (a^i + b^j)

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\frac{2}{3} (a^i - b^j)

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Solution

The correct option is A $\frac{1}{3} (a^i + b^j)$
The center of mass will be at the centroid of the given triangle. The coordinates of the centroid are $(\frac{0 + a + 0}{3}, \frac{0 + 0 + b}{3}) = (\frac{a}{3}, \frac{b}{3})$ . Hence correct option is A.

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Three particles, each of mass m, are placed at the corner of right angle triangle as shown in the figure. if OA=a and OB=b, the position vector of the centre of mass is : (here ^i and ^j are unit vector along x and y axes, respectively )

The correct option is A 13(a^i+b^j)The center of mass will be at the centroid of the given triangle. The coordinates of the centroid are (0+a+03,0+0+b3)=(a3,b3). Hence correct option is A.

Three particles, each of mass m, are placed at the corner of right angle triangle as shown in the figure. if OA=a and OB=b, the position vector of the centre of mass is :
(here $^i$ and $^j$ are unit vector along x and y axes, respectively )

The correct option is A $\frac{1}{3} (a^i + b^j)$
The center of mass will be at the centroid of the given triangle. The coordinates of the centroid are $(\frac{0 + a + 0}{3}, \frac{0 + 0 + b}{3}) = (\frac{a}{3}, \frac{b}{3})$ . Hence correct option is A.