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Longitudinal Stress

A rod of leng...

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A rod of length 4 m is suspended from two wiresas shown in figure. One of them is made of steeland other of copper of cross-sectional area 10-2m2and 4 x 10-2 m2. Find distance x if equal stress isexperienced by both the wires (Yand Ycopper=2x 1011 N/m2Steel1.1 x 1011 N/m2SteelCopperW(2) 3.5 m(1) 2 m(4) 3 m(3) 3.2 m

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Q. A light rod of length

2.00 m

is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel of cross-section

10^{- 3} m^{2}

and the other is of brass of cross-section

2 \times 10^{- 3} m^{2}

. Find out the position along the rod at which a weight may be hung to produce equal stress in both the wires.

Y_{steel} = 2 \times 10^{11} {N/m}^{2}

Y_{brass} = 10^{11} {N/m}^{2}

Q. A light rod of length

2 m

is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to it ends. One of the wire is made of steel and it's cross section is

10^{- 3} m^{2}

and the other is of brass of cross section

2 \times 10^{- 3} m^{2}

. The position along the rod at (from the end where brass wire is tied) which a weight may be hung to produce equal stress on both wires

(Y_{s t e e l} = 2 \times 10^{11} {Nm}^{- 2}; Y_{b r a s s} = 10^{11} {Nm}^{- 2})

A B

2 m

is suspended from the ceiling horizontally by means of two vertical wires as shown in Fig. One of the wires is made of steel of cross-section

0.1 {cm}^{2}

and the other of brass of cross-section

0.2 {cm}^{2}

. The Young's modulus of brass is

1.0 \times 10^{11} {Nm}^{- 2}

and of steel is

2.0 \times 10^{11} {Nm}^{- 2}

W

is hung at point

C

x

A

. It is found that the stress in the two wires is the same when

x = \frac{n}{3} metre

. Find the value of

n

Q. A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of the stresses developed in steel and copper wire

Y

2 \times 10^{11} {N/m}^{2}

Y

1.3 \times 10^{11} {N/m}^{2}

Q. An Aluminium and Copper wire of same cross sectional area but having lengths in the ratio

2 : 3

are joined end to end. This composite wire is hung from a rigid support and a load is suspended from the free end. If the increase in length of the composite wire is

2.1 m m

, the increase in lengths of Aluminium and Copper wires are : [

Y_{A l} = 20 \times 10^{11} N / m^{2}

Y_{C u} = 12 \times 10^{11} N / m^{2}

]

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