In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is
(g = gravitational acceleration)

Question

In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is

(g = gravitational acceleration)

G1 Physics · Accepted Answer

From the figure, at the point where the tension becomes zero, the radius makes 60° with the downward vertical. Let the speed at this point be v. Radially toward the centre, T + mg cos60° = mv²/r. Since T = 0, mg(1/2) = mv²/r. Hence, v² = gr/2. The vertical height of this point above the bottom point A is h = r + r cos60° = r + r/2 = 3r/2. Let the speed at the bottom be u. By conservation of mechanical energy between the bottom and the zero-tension point, ½ μ \mu μ ² = mgh + ½mv². Therefore, u²…