Q. A heavy mass is attached to a thin wire and is whireled in a vertical circle. The wire is most likely to break

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Solution:

When the mass is at the lowest point.
Explanation The Force acting on the Particles will be maximum in case of the Vertical circle when the Force acting will be in the direction of its tension force of string.
When this situation arises then,
Tension
Force will be maximum at this position and there will likely be more chances to break.
This case will be there when the mass is at the lowest position.