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A sphere of mass m attached with the fre...

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)))`

Text Solution

Verified by Experts

The correct Answer is:
D
`Delta l = ((F_("net")l))/(YA) , V = sqrt(2gl)`
`= ((mg + (mv^(2))/(l))l)/(YA) = ((mg + 2mg)l)/(YA)`
`Deltas L = (3mgl)/(Y(pi r^(2))), v = (1)/(2)Fe, U = (YA)/(2l) xx (Delta l)^(2) = (9m^(2) g^(2) l)/(2Y pi r^(2))`
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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 veritcle plane form the horizontal positon. Elastic energy should in the wire in the vericle positon is

    A
    `(9m^(2) g^(2)l)/(2Ypi r^(2))`
    B
    `(7m^(2) g^(2)l)/(2Ypi r^(2))`
    C
    `(9m^(2) g^(2)l)/(Ypi r^(2))`
    D
    `(9m^(2) g^(2)l)/(4Ypi r^(2))`

  • A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed . The elongation of the wire is l .

    A
    Loss in gravitational potential energy of` M` is `Mgl`
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    The elastic potential energy stored in the wire is ` Mgl`
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    D
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