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A wire of length 1m fixed at one end has...

A wire of length `1m` fixed at one end has a sphere attached to it at the other end. The sphere is projected hroizonatally with a veloicity of `sqrt(9g)`. When it decribes a vertical circle the ratio of elongations of the wire when the sphere is at top and bottom of the circle is

A

`2:5`

B

`5:2`

C

`3:5`

D

`5:3`

Text Solution

Verified by Experts

The correct Answer is:
A
`V_("top") = sqrt(xrg), V_("bottom") = sqrt((x+4)rg)`
`V_("top") = sqrt(5g) , v = sqrt(9gr)`
`T_("bottm") = (mv_(b)^(2))/(r) + mg = 10mg`
`T_("top") = (mv_(t)^(2))/(r)-mg = 4mg, (e_(t))/(e_(b)) = (4mg)/(10mg)`
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Knowledge Check

  • A sphere of mass m attached with the free end of a steel wire of length l swings in the veritical plane form the horizontal positon. Elongation of the wire in the vericle positon is

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    `(3mgl)/(Y(pi r^(2)))`

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