Figure shows the graph of elastic potent...

Figure shows the graph of elastic potential energy `(U)` stored versus extension, for a steel wire `(Y = 2xx10^(11) Pa)` of volume `200 c c`. If area of cross- section `A` and original length L, then

`A = 10^(-4) m^(2)`

`A= 10 ^(-3) m^(2)`

`L=1.5 m`

`L = 2 m`

Text Solution

Verified by Experts

The correct Answer is:

A, D

`U =1/2 kx^(2)` . It is a parabola symmetric about
U- axis .
At `x = 0.2 mm`, `U =0.2 J` ( from the figure )
`:. 0.2 = 1/2 k(2xx10^(-4))^(2)`
`rArr k = (YA)/(L) `
`(A)/L = (K)/(Y) = (10^(7)) Nm^(-1)`
`k = (YA)/(L)`
`rArr (A)/(L) = (k)/(Y) = (10^(7))/(2xx10^(11)) = 5xx10^(-5)` ...(i)
`AL = "Volume" = 200xx10^(-6) m^(3)` ...(ii)
On solving Eqs. (i) and (ii) , We get
`A= 10^(-4) m^(2)` and `L = 2 m`

Topper's Solved these Questions

ELASTICITY
DC PANDEY|Exercise Level 2 Comprehension Based|6 Videos
ELASTICITY
DC PANDEY|Exercise Level 2 Subjective|10 Videos
ELASTICITY
DC PANDEY|Exercise Level 2 Single Correct|10 Videos
CURRENT ELECTRICITY
DC PANDEY|Exercise All Questions|434 Videos
ELECTROSTATICS
DC PANDEY|Exercise Integer|17 Videos

Figure shows the graph of elastic potential energy (U) storeed versus, extension, for a steel wire (Y = 2xx10^(11) pa) of volume 200cc . Find the original length of the wire

`4m`

`2m`

`4cm`

`2cm`

In CGS system, the Young's modulusm of a steel wire is 2 xx 10^(12) . To double the length of a wire of unit cross-section area, the force

`4 xx 10^(6)` dynes

`2 xx 10^(12)` dynes

`2 xx 10^(12)` newtons

`2 xx 10^(8)` dynes

Select and write the corrcet answer : The elastic potential energy per unit volume in a copper wire (Y = 1.2 xx 10^(11) Pa) stretched by 0.5 % of its length is

`1.5 xx 10^(10) J//m^(3)`

`1.5 xx 10^(8) J//m^(3)`

`1.5 xx 10^(7) J//m^(3)`

`1.5 xx 10^(6) J//m^(3)`