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
[2000]
(a) bottom point $B$
(b) the point $C$
(c) the point $D$
(d) top point $A$
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Solution:
- (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 $B$ ]
