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Question

A wire of length 1 m fixed at one end has a sphere attached to it at the other end. The sphere is projected horizontally with a velocity of 9g. When it describes a vertical circle, the ratio of elongations of the wire when the sphere is at the top and bottom of the circle is :

A
2:5
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B
5:2
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C
3:5
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D
5:3
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Solution

The correct option is A 2:5
When sphere is at top point, it's kinetic energy will be kinetic energy at bottom - raise in potential energy
So, K.Etop=K.E.bottomP.E.

=12mvb2mgh
=12m9gmg(2r)
=92mg2mg (r=1)
=52mg
K.E.=12mvt2
52mg=12mvt2vt=5g
So, tension in top position is: mvt2rmg=5mgmg=4mg
And tension in bottom position is: mvb2r+mg=9mg+mg=10mg
So, Y=F/AΔl/l
Δl=FlAY
So, ΔlF
ΔltΔlb=FtFb=4mg10mg=25

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