Two spheres of equal masses are attached to a string of length 2 m as shown in figure. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. What is the value of the ratio:

Explanation

Let the balls of the two circles are `r_(1) and r_(2)`. The linear speed of the two masses are `v_(1) = omega r_(1), v_(2) = omega r_(2)` where `omega` is the angular speed of the circular motion. The tension in the strings are such that
`T_(2) = (mv_(2)^(2))/(r_(2)) = m omega^(2) r_(2)`
`T_(1) - T_(2) = (mv_(1)^(2))/(r_(1)) = m omega^(2) r_(1)`
`therefore T_(1) = m omega^(2) r_(1) + T_(2) = m omega^(2) (r_(1) + r_(2))`
`therefore (T_(1))/(T_(2)) = (r_(1) + r_(2))/(r_(2)) = (1 + 2)/(2) = (3)/(2)`