Can someone solve 44 A small ball is tied to a string and set rotating with negl
ID: 3278283 • Letter: C
Question
Can someone solve 44 A small ball is tied to a string and set rotating with negligible friction in a vertical circle. Prove that the tension in the string at the bottom of the circle exceeds that at the top of the circle by eight times the weight of the ball. Assume the ball's speed is zero as it sails over the top of the circle and there is no additional energy added to the ball during rotation. Potential Energy Diagrams and Stability A mysterious constant force of 10 N acts horizontally on everything. The direction of the force is found to be always pointed toward a wall in a big hall. Find the potential energy of a particle due to this force when it is at a distance x from the wall, assuming the potential energy at wall to be zero.Explanation / Answer
44) since velocity at top is zero
Centripetal force =mv^2 /R = 0
T - mg = 0
T = mg
Now change in KE at bottom by energy conservation = mg*2R
= 2 mgR
0.5 mv^2 +0.5 iw^2 = 2mgR
0.5 mv^2 = 2 mgR
T - mg = 2mg/0.5
T = 5mg
It exceeds the tension at the top by 4mg i.e. 4 times the weight.
It can be eight time only if the radius of ball is not negligible
as compared to the radius of the vertical circle. The radii should be given in that case.