Particles Connected By Inestensible String Moving in a Circle

Suppose we have two particles connected by a light inextensible string moving in a circle around a common centre. The centre of the circle and the particles lie in a straight line. What will be the tension in each string?

  for each particle:
Particle 1:  
\[m_1 \omega^2 r_1=T_1-T_2\]

Particle 2:  
\[m_2 \omega^2 r_2=T_2\]

From the second of these, Particle 1:  
\[T_2=m_2 \omega^2 r_2\]

Then from the first Particle 1:  
\[T_1=m_1 \omega^2 r_1+T_2=m_1 \omega^2 r_1+m_2 \omega^2 r_2=\omega^2(m_1r_1+m_2r_2)\]

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