Motion in a Plane - Result Question 52

55. A small sphere is attached to a cord and rotates in a vertical circle about a point $O$. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at

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(a) bottom point $B$

(b) the point $C$

(c) the point $D$

(d) top point $A$

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Solution:

  1. (a) In the case of a body describing a vertical circle,

$T-mg \cos \theta=\frac{mv^{2}}{l} ; T=m g \cos \theta+\frac{m v^{2}}{l}$

Tension is maximum when $\cos \theta=+1$ and velocity is maximum

Both conditions are satisfied at $\theta=0^{\circ}$ (i.e., at lowest point $B$ ]