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.

A system consists of three particles located at the corners of a right

1.	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.
Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_NEO_CAO_PHY_XI_V01_MP2_C07_SLV_012_S01.png" width="80%"/> <br/> Using the <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> <br/> `X_(c)=(summ_(i)x_(i))/(M)=(2md+m(b+d)+3m(d+b))/(<a href="https://interviewquestions.tuteehub.com/tag/6m-332078" style="font-weight:bold;" target="_blank" title="Click to know more about 6M">6M</a>)=d+(2//<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)b` <br/> `Y_(c)=(summ_(i)y_(i))/(M)=(2m(o)+m(o)+<a href="https://interviewquestions.tuteehub.com/tag/3mh-1863494" style="font-weight:bold;" target="_blank" title="Click to know more about 3MH">3MH</a>)/(6m)=<a href="https://interviewquestions.tuteehub.com/tag/h-1014193" style="font-weight:bold;" target="_blank" title="Click to know more about H">H</a>//2` <br/> `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 <br/> `vecr_(c)=X_(c)hati+Y_(c)hatj+Z_(c)hatk,vecr_(c)=(d+(2)/(3)b)hati+(h)/(2)hatj`</body></html>