Asmall metal ball is suspended from the ceiling by a thread of negligible mass. the ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone. the acceleration of gravity is 9.8 m/s 2 . how long does it take for the ball to rotate once around the axis?

Time taken,

Explanation:

It is given that, a small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone as shown in attached figure.

From the figure,

The sum of forces in y direction is :

Sum of forces in x direction,

.............(1)

Also,

Equation (1) becomes :

...............(2)

Let t is the time taken for the ball to rotate once around the axis. It is given by :

Put the value of T from equation (2) to the above expression:

On solving above equation :

Hence, this is the required solution.