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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

Vikas TU
14149 Points
7 months ago
Dear Student,
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
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