Home
Class 12
PHYSICS
A steel wire 4 m in length is stretched ...

A steel wire 4 m in length is stretched through 2mm. The cross-sectional area of the wire is `2.0 mm^(2)`. If Young's modulus of the steel is `2xx10^(11) Nm^(-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 ENGLISH|Exercise Try Yourself|32 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

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

  • MECHANICAL PROPERTIES OF FLUIDS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J|9 Videos

  • Mock test 03

    AAKASH INSTITUTE ENGLISH|Exercise EXAMPLE|44 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 energy density of wire, (b) the elastic potential energy stored in the wire.

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 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 2.0 m 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 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 a wire is 2 xx 10^(11)N//m^(2) . If a stress of 2 x 108 N/m2 is applied at the free end of a wire, find the strain in the wire.

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)

The Young's modulus of the material of a wire is 2xx10^(10) N m^(-2) If the elongation strain is 1% then the energy stored in the wire per unit volume in J m^(-3) is

(a) A wire 4 m long and 0.3 mm, calculate the potential energy stored in the wire. Young's modulus for the material of wire is 2.0xx10^(11) N//m^(2) .