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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

    A
    `(mgl)/(Y(pi r^(2)))`
    B
    `(2mgl)/(Y(pi r^(2)))`
    C
    `(mgl)/(3Y(pi r^(2)))`
    D
    `(3mgl)/(Y(pi r^(2)))`

  • A steel wire of 1.5 m long and of radius 1 mm is attached with a load 3 kg at one end the other end of the wire is fixed it is whirled in a vertical circle with a frequency 2 Hz. Find the elongation of the wire when the weight is at the lowest position Y=2xx10^(11)N//m^(2) and (g=10m//s^(2))

    A
    `1.77xx10^(-3)m`
    B
    `7.17xx10^(-3)m`
    C
    `3.17xx10^(-7)m`
    D
    `1.37xx10^(-7)m`

  • A copper wire of negligilble mas, length (l) and cross-sectional area (A) is kept on a smooth horizontal table with one end fixed, a ball of mass 'm' is attached at the other end. The wire and the ball are rotated with angular velocity 'omega' . If wire elongates by Delta l then the Young's modulus of wire and if on incresing the angular velocity from omega to omega^(1) when the wire breaks-down, then the brekaing stress (Deltal lt lt l ) are respectivley.

    A
    `((m l^(2) omega^(2)))/(A Delta l), (ml omega^(2))/(A)`
    B
    `(ml)/(A Delta l omega^(2)), (ml omega^(2))/(A)`
    C
    `(ml omega^(2))/(A Delta l ), (m omega^(2))/(Al)`
    D
    `(ml omega^(2))/(A Delta l ), (ml omega^(2))/(Al)`
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