Question

Two spheres of masses M and m equal to 9 and 3 g, respectively, are joined by strings AO and OB of a total length of 1 m to a vertical axis O (Fig. ) and are made to rotate in an horizontal plane about the axis with a uniform angular velocity co. Find the ratio of the lengths of string for which their tensions will be the same. Neglect the weight of the strings

Answer 1

Explanation:

The centripetal force acting on M is F1 = ω2Mx (Fig. 216). The force acting on m is F2 = ω2m(l - x). Since F1 is to be equal to F2 , then

The distances of the spheres from the centre of gravity of the system are also determined by similar expressions. The tensions in the strings are equal when the centre of rotation coincides with the centre of gravity of the system.