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The pressure that has to be applied to...

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by `100^(@)C`is :
(For steel Young's modulus is `2 xx 10^(11)N m^(-2)` and coefficient of thermal expansion is`1.1 xx 10^(-5) K^(-1)`)

A

`22xx10^(7)atm`

B

`2.2xx10^(3)atm`

C

zero

D

`4.3xx10^(3)atm`

Text Solution

Verified by Experts

The correct Answer is:
B
If the rod is allowed to expand then it will expand by `/_\l=lalpha /_\T` due to increase in temperature by `/_\T`. But as the length of the cylinder is kept constant by applying pressure, a stress is developed in te cylinder. The decrease in length of cylinder due to elasticity is `/_\l=l alpha/_\T ` and a compressive stress will develop it.
Stress=Excess pressure applied at ends
`=Yxx(/_\l)/lYalpha/_\T`
`=2xx10^(11)xx11xx10^(-6)xx10=2.2xx10^(3)atm`
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The pressure that has to be applied to the ends of a steel wire of length 10cm to keep its length constant when its temperature is raised by 100^@C is : (For steel Young's modulus is 2xx10^11 Nm^-2 and coefficient of thermal expansion is 1.1xx10^-5K^_1 )

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A steel wire of length 4 m and diameter 5 mm is strethed by 5 kg-wt. Find the increase in its length, if the Young's modulus of steel is 2xx10^(12) dyne cm^(2)

Young 's modulus of steel is 2.0 xx 10^(11)N m//(2) . Express it is "dyne"/cm^(2) .

A uniform steel wire of cross-sectional area 0.20 mm^2 is held fixed by clamping its two ends. Find the extra force exerted be each clamp on the wire if the wire is cooled from 100^0C to 0^o C . Young's modulus of steel = 2.0 xx 10^11 N m^(-2) . Coefficient of linear expansion of =1.2 xx 10^(-5) C^(-1) .

A steel wire of length 600cm and diameter 1.2 mm is stretched through 4 mm by a load. Calculate the work done. Young's modulus of steel = 2xx 10^(11) Nm^(-2) .

A steel wire of length 4 m and diameter 5 mm is stretched by 5kg-wt. Find the increase in its length if the Young's modulus of steel wire is 2.4 xx 10^(12) dyn e cm^(-2)

There is same change in length when a 33000 N tensile force is applied on a steel rod of area of cross-section 10^(-3)m^(2) . The change of temperature reuired to produce the same elongation, if the steel rod is heated , if (The modulus of elasticitay is 3xx10^(11) N//m^(2) and the coefficient of linear expansion of steel is 1.1 xx 10^(-5) //^(@)C ).

At 50^(@)C , a brass rod has a length 50 cm and a diameter 2 mm . It is joined to a steel rod of the same length and diameter at the same temperature . The change in the length of the composite rod when it is heated to 250^(@)C is (Coefficient of linear expansion of brass = 2.0 xx 10^(-5)"^(@) C^(-1) , coefficient of linear expansion of steel = 1.2 xx 10^(-5) "^(@) C^(-1) )

What force is required to stretch a steel wire to double its length when its area of cross section 1 cm2 and Young.s modulus 2 xx 10^(11)N//m^(2) .

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