As shown in the figure a ball of mass 125 kg is connected by

As shown in the figure, a ball of mass 1.25 kg is connected by means of two massless strings, each of length D = 1.8 m. to a vertical rotating rod. The strings are tied to the rod with separation L = 1.8 m and are taut. The tension in the upper string is 31.5 N. What are the. tension in the lower string? magnitude of the net force on the ball? What is the speed of the ball? What is the direction of the net force?

Solution

The vertical component = 31.5 sin 30° = 15.75 N

As the ball weighs 12.5 N, vertical component = 15.75 - 12.5 = 3.25 N

T sin 30 = 3.25

Tension in lower string T = 6.5 N

---------------------------------------------------

The horizontal component of the tensions constitute the centripetal force.

(31.5 + 6.5) cos30 = m v² / l cos30°

------------------------------------------------

Magnitude of net force = sum of horizontal components

= (31.5 + 6.5) cos30

= 32.91 N

------------------------------------------------

Direction of net force = 0

[ as the sphere is in uniform circular motion so no vertical forces ]