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A stationlay unifrom sting of modlulus Y...

A stationlay unifrom sting of modlulus `Y`, density `rho` and length `'I'` is hanging from a rigid support.
The stress at a distance `x` from the point of tis suspension.

A

`rho x g`

B

`rho(l-x)g`

C

`rho lg`

D

`(rho x^(2) g)/(l)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let us take the point `P` at a distance `x` form the `O` of suspendsion of the stirng
Let us tension in the string at `P` be `T`. We can see that the shaded portion of the string is in equilibrium under the action of `m" g darr` and `T uarr`, where `m" = "mass"` of the shaded portion fo the string. Then applying Newton's secondlaw,
`F = ma`, wherea `= 0` and `F = T - m" g`,
we have `T = m"g,` substituing
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Knowledge Check

  • A thick rope of density rho and length L is hung from a rigid support. The increase in length of the rope due to its own weight is ( Y is the Young's modulus)

    A
    `0.1/(4Y)rhoL^(2)g`
    B
    `1/(2Y)rhoL^(2)g`
    C
    `(rhoL^(2)g)/Y`
    D
    `(rhoLg)/Y`

  • A chain of mass M and length L is held vertical by fixing its upper end to a rigid support. The tension in the chain at a distance y from the rigid support is:

    A
    `Mg`
    B
    `Mg(L-y)//L`
    C
    `MgL//(L-y)`
    D
    `Mgy//L`

  • A unifrom steel rod of length 1m and area of cross-section 20 cm^(2) is hanging from a fixed support. Find the increases in the length of the rod.

    A
    `1.923xx10^(-5)cm`
    B
    `2.923xx10^(-5)cm`
    C
    `1.123xx10^(-5)cm`
    D
    `3.123xx10^(-5)cm`