Question

A particle of mass $m_1$ is tightened to one end of a string and another one of mass $m_2$ to the middle point; the other end of the string being tightened to a fixed point on a smooth horizontal table. The particles are then projected so that the two portions of the string are always in the same straight line and describe horizontal circles. Find the ratio of the tension in the two parts of the string.

Answer 1

w = angular velocity

$r_2=\frac{l}{2}$

$r_1=l$

$T_2=T_1+\frac{m_2{w}^{2}l}{2}$

$T_1=m_1{w}^{2}l+\frac{m_2{w}^{2}l}{2}$

$\frac{T_1}{T_2}=\left(\frac{2m_1}{2m_1+m_2}\right)$