Question

If three point masses 100g 150g and 200g are situated at the verticies of an equvilateral triangle of side 0.5 then what will be the coordinates of the centre of mass of the system

Answer 1

Given that,

Given that,  m1=100g

Given that,  m1=100g m2=150g

Given that,  m1=100g m2=150g m3=200g

Given that,  m1=100g m2=150g m3=200ga = 0.5 m = 50 cm

Given that,  m1=100g m2=150g m3=200ga = 0.5 m = 50 cmNow, according to diagram

Given that,  m1=100g m2=150g m3=200ga = 0.5 m = 50 cmNow, according to diagramCenter of mass coordinates

Given that,  m1=100g m2=150g m3=200ga = 0.5 m = 50 cmNow, according to diagramCenter of mass coordinates  Ycm=0×100+150×50+200×25÷450

 Ycm=7500+5000÷450

 Ycm=27.8cm

=27.8cm Ycm=0.28m

=0.28mNow,

=0.28mNow,  Ycm=4500×100+0×150+3×25×200

=0.28mNow,  Ycm=4500×100+0×150+3×25×200 Ycm=4508660.3

=0.28mNow,  Ycm=4500×100+0×150+3×25×200 Ycm=4508660.3 Ycm=19.2cm

=0.28mNow,  Ycm=4500×100+0×150+3×25×200 Ycm=4508660.3 Ycm=19.2cm Ycm=0.2m

=0.28mNow,  Ycm=4500×100+0×150+3×25×200 Ycm=4508660.3 Ycm=19.2cm Ycm=0.2mHence, the center of mass of three particles at the vertices of an equilateral triangle is Xcm=0.28cm and Ycm=0.2cm  respectively