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Three particles each of mass m are placed at the three corners of an equilateral triangle of side a. The work done on the system to increase the sides of the triangle to 2a is:

Answer» <html><body><p></p>Solution :The center of mass of an equilateral triangle <a href="https://interviewquestions.tuteehub.com/tag/lies-1073086" style="font-weight:bold;" target="_blank" title="Click to know more about LIES">LIES</a> at its geometrical center G. The positions of the mass m,, m, and m, are at positions A, B and C as shown in the Figure. From the given position of the masses, the coordinates of the masses mand m, are easily marked as (0,0) and (1,0) espectively.<br/> To find the position of m, the Pythagoras theorem is applied. A As the ADBC is a right angle triangle, <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FM_PHY_XI_V01_C05_SLV_024_S01.png" width="80%"/> <br/> `<a href="https://interviewquestions.tuteehub.com/tag/bc-389540" style="font-weight:bold;" target="_blank" title="Click to know more about BC">BC</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)=CD^(2)+DB^(2)` <br/> `CD^(2)=BC^(2)-DB^(2)` <br/> `CD^(2)=1^(2)-((1)/(2))^(2)=1-((1)/(4))=(3)/(4)` <br/> `CD=(sqrt(2))/(2)` <br/> The position of mass `m_(3)` is `((1)/(2), (sqrt(3))/(2)) or (0.5, 0.35 sqrt(3))` <br/> X coordinate of center of mass, <br/> `X_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))` <b> `m_(1)+m_(2)m_(3))` <br/> `X_(CM)=((1xx0)+(2xx1)+(3xx0.5))/(1+2+3)=(35)/(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>),X_(CM)=(7)/(12)m` <br/>x-coordinate of center of mass, <br/> `Y_(CM)=(m_(1)y_(1)+m_(2)y_(2)+m_(2)m_(3)y_(3))/(m_(1)+m_(2)+m_(3))` <br/> `Y_(CM)=((1xx0)+(2xx0)+(3xx0.5xx sqrt(3)))/(1+2+3)=(1.5 sqrt(3))/(6)`<br/> `Y_(CM)=(sqt(3))/(4)m` <br/> `:.` The coordinates of center of mass Grey) is `x_(CM),y_(CM)` is `((7)/(12), (sqrt(7))/(4))`</b></body></html>


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