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a wire of length 1m is fixed at one end has a sphere attached to it at the other end .the sphere is projected horizontally with a velocity of root9g.when it describes a vertical circle ,the ratio of elongations of the wire when the sphere is at top and bottom of the circle is

a wire of length 1m is fixed at one end has a sphere attached to it at the other end .the sphere is projected horizontally with a velocity of root9g.when it describes a vertical circle ,the ratio of elongations of the wire when the sphere is at top and bottom of the circle is

Grade:11

1 Answers

Vikas TU
14149 Points
7 months ago
Dear Student,
Please find below the solution to the asked query:
Given that the velocity of the particle at the bottom is √9g.
Therefore, the tension in the string at the bottom is,
Tb=mg+mv^2/l=mg+9mg
⇒Tb=10 mg

Let V be the velocity of the sphere, when it is at the top of the circle, then
1/2 * m(V^2i−V^2f)=mg(2l)⇒V^2 = 9g−4g 
⇒V= √5g
So, tension in the string. When it is top is,
Ttop=mVt^2/l −mg=5mg−mg
⇒Ttop=4mg
Therefore, the ratio of tension, when the sphere is at top and bottom is,
Ttop/Tbot=4mg/10mg=2/5 
Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards

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