If a person whirls an object horizontally in a counter clockwise direction and the string breaks at point p as shown, what path will the rock follow?

when an object is revolving in circular path then its velocity is always along the tangent of the circular path

so while moving in circular path if the string is break then due to law of inertia the object will always move in the direction of initial motion

As we know that as per law of inertia if an object will not change its state of motion or state of rest until some external force will act on it.

So here also the object will move along its tangential direction once the string will break

so here the correct path will be

Option B

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