A 4.6 m massless rod is loosely pinned to a frictionless pivot at 0. A 8.7 kg ba

Question

A 4.6 m massless rod is loosely pinned to a frictionless pivot at 0. A 8.7 kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely in a vertical circle between A and B. In the figure, the tension in the rod when the ball passes through the lowest point at D is closest to:

348 N

The answer is 348 N but when I solve I always get 261 N.

348 N

The answer is 348 N but when I solve I always get 261 N.

Explanation / Answer

we know, F = ma
At the Lowest Point D -
T - mg = mv^2/r
T = m(g+v^2/r) ----------1

Using Energy Conservation -
Potential Energy = Kinetic Energy
mgh = 1/2 mv^2
v^2 = 2gh

where h = r + r sin(theta)

v^2 = 2gr(1+sin(theta))

Substituing Value in eq 1

T = mg(1+2(1+sin(theta)))
T = mg(3 + 2*sin(30))
T = mg (3 + 2*1/2)
T = 4*mg
T = 4 * 8.7 * 10 N
T = 348 N

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