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A system consists of three particles loc...

A system consists of three particles located at the corners of a right triangle as shown in the figure. Find the position vector of centre of mass of the system.

Text Solution

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Using the equation
`X_(c)=(summ_(i)x_(i))/(M)=(2md+m(b+d)+3m(d+b))/(6m)=d+(2//3)b`
`Y_(c)=(summ_(i)y_(i))/(M)=(2m(o)+m(o)+3mh)/(6m)=h//2`
`Z_(c)=0`, because the particles are in X - Y plane we can express the position of centre of mass from the origin using a position vector as
`vecr_(c)=X_(c)hati+Y_(c)hatj+Z_(c)hatk,vecr_(c)=(d+(2)/(3)b)hati+(h)/(2)hatj`
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