Circular Motion · Physics · IAT (IISER)

On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves with a constant speed. Vani starts with a constant acceleration from rest. They meet again on the track with the same speed. Which of the following is correct?

A point mass $m$ attached to a massless string is undergoing circular motion in a vertical plane. The length of the string is $R$ and the acceleration due to gravity is $g$. If the minimum value of the tension in the string is 2 mg , the maximum speed of this circular motion of the point mass is