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One end of a uniform wire of length 'L...

One end of a uniform wire of length `'L'` and mass `'M'` is attached rigidly to a point in the roof and a load of a mass `'m'` is suspended from its lower end. If `A` is the area of cross-section of the wire then the stress in the wire at height `'x'` from its lower end `(x lt L)` is

A

`(Mg)/(A) + (mxg)/(AL)`

B

`(mg)/(A) - (Mxg)/(AL)`

C

`(mg)/(A) + (Mxg)/(AL)`

D

`(mg)/(AL) + (Mxg)/(A)`

Text Solution

Verified by Experts

The correct Answer is:
C
Tension in the string at point `'P'` is
`TY = wt` of load `+ wt` of wire of length `'x'`
`T = mg + (M)/(L) xg`, Stress at `P = (T)/(A) = (mg)/(A) + (Mxg)/(AL)`
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Knowledge Check

  • One end of a unifrom wire of length L and weigth W is attached rigidly to a point in the roof and a weight W_(1) is suspended from its lower end. If S is the area of cross-section of the wire then the stress in the wire at a height (3L)/(4) from its lower end is

    A
    `((W_(1) + W))/(S)`
    B
    `(W_(1))/(S)`
    C
    `((W_(1) + (3W)/(4)))/(S)`
    D
    `((W_(1) + (W)/(4)))/(S)`

  • One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W_(1) is suspended from its lower end. If A is the area of cross-section of the wire, the stress in the wire at a height 3L//4 from its lower end is

    A
    `W_(1)/(A)`
    B
    `(W_(1)+(W//4))/(A)`
    C
    `(W_(1)+(3W//4))/(A)`
    D
    `(W_(1)+W)/(A)`

  • One end of uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W_(1) is suspended from its lower end. If s is the area of cross section of the wire, the stress in the wire at a height ( 3L//4 ) from its lower end is

    A
    `(W_(1))/s`
    B
    `[W_(1)+W/4]s`
    C
    `[W_(1)+(3W)/4]//s`
    D
    `(W_(1)+W)/s`
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