A ball of mass m is fastened to a string. The ball swings at constant speed in a vertical circle of radius R with
the other end of the string held fixed. Neglecting air resistance, what is the difference between the string's
tension at the bottom of the circle and at the top of the circle?
(A) mg (B) 2mg (C) 4mg (D) 8mg
Answers
Answer:
2mg
Explanation:
as on the bottom of the vertical circle
the net force acting downwards will be equal to the sum of the weight and centrifugal force acting on the object due to circular motion, this downward force will be equal to tension to balance to maintain the vertical circle
Net Force Downwards = Force(centrifugal) + weight = Tension 1 to balance
Net Force Downwards = Force(centrifugal) + mg = Tension 1 to balance
now, on top of the circle, the centrifugal and weight be on the opposite sides
Net Force upward = Force(centrifugal) - mg = Tension 2 to balance
difference in the tension 1 and tension 2
Tension 1 - Tension 2 = Force(centrifugal) + mg - (Force(centrifugal) - mg)
Tension 1 - Tension 2 = Force(centrifugal) + mg - Force(centrifugal) + mg