Home
Class 12
PHYSICS
A steel wire of 4.0 m in length is stret...

A steel wire of 4.0 m in length is stretched through 2.00 mm. The cross-sectional area of the wire is `2.0mm^(2)` if young's modulus of steel is `2.0xx10^(11)N//m^(2)` find (i) the energy density of wire (ii) the elastic potential energy stored in the wire.

Text Solution

Verified by Experts

Here, `l = 4.0 m, Deltal = 2 xx 10^-3 m, a = 2.0 xx 10^-6 m^2 Y = 2.0 xx 10^11 Nm^-2`
(i) The energy density of stretched wire `(DeltaU)/(Volume)=1/2 stressxx strain`
`(1)/(2)xxYxx(strain)^(2)`
`=(1)/(2)xx2.0xx10^(11)Nm^(-2)xx((2xx10^(-3))/(4))^(2)`
`=2.5xx10^4 j//m^(3)`
Elastic potential energy = energy density `xx` volume
`= (2.5xx 10^(4)j//m^3)xx (8.0 xx:10^6 m^3)`
= 0.20 J
Promotional Banner

Topper's Solved these Questions

  • MECHANICAL PROPERTIES OF SOLIDS

    AAKASH INSTITUTE|Exercise Try Yourself|32 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A)|31 Videos

  • MECHANICAL PROPERTIES OF FLUIDS

    AAKASH INSTITUTE|Exercise SECTION - J|9 Videos

  • Mock test 03

    AAKASH INSTITUTE|Exercise EXAMPLE|37 Videos

Similar Questions

Explore conceptually related problems

A steel wire of 4.0 m is stretched through 2.0 mm. The cross - sectional area of the wire is 2.0 mm^2. If young's modulus of steel is 2.0 xx10^(11) Nm^(-2) find (i) the energy density of the wire, (ii) the elastic potential energy stored in the wire.

A steel wire 4.0m in length is stretched through 2.0mm .The cross -sectional area of the wire is 2.0 mm^(2) .If young's modulus of steel is 2.0xx10^(11) N//m^(2) (a) the enrgy density of wire, (b) the elastic potential energy stored in the wire.

A steel wire 4.0 m in length is stretched through 2.0 mm. The cross-sectional area of the wire is 2.0 mm^(2) . If young's modulus of steel is 2.0 xx 10^(11) Nm^(-2) , then find the energy density of wire.

A steel wire of length 5 m and area of cross-section 4 mm^(2) is stretched by 2 mm by the application of a force. If young's modulus of steel is 2xx10^(11)N//m^(2), then the energy stored in the wire is

The area of a cross section of steel wire is 0.1cm^2 and Young's modulus of steel is 2xx10^(11)Nm^-2 . The force required to strech by 0.1% of its length is

The area of a cross-section of steel wire is 0.1 cm^(-2) and Young's modulus of steel is 2 x 10^(11) N m^(-2) . The force required to stretch by 0.1% of its length is

A steel wire of length 2.0 m/s is stretched through 2.0 mm. The cross sectional area of the wire is 4.0 mm^2. Calculate the elastic potential energy stored in the wire in the stretched condition. Young modulus of steel =2.0x10^11Nm^-2

A steel wire of length 3.0m is stretched through 3.0 mm. the cross-sectional area of the wire is 5.0mm^(2) . Calculate the elastic potential energy stroed in the wire in the stretched condition. Young's modulus of steel is 2.0 xx 10^(11) Nm^(-2) .

A steel wire of length 4 m and diameter 5 mm is stretched by kg-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)

A wire of length 1m is stretched by a force of 10N. The area of cross-section of the wire is 2 × 10^(–6) m^(2) and Y is 2 xx 10^(11) N//m^(2) . Increase in length of the wire will be -