You visited us 152 times! Enjoying our articles? Unlock Full Access!

Young's Modulus of Elasticity

The length of...

Question

The length of a metal wire is $l_{1}$ when the tension in it is $F_{1}$ and $l_{2}$ when the tension in it is $F_{2}$ . The natural length of the wire is

\frac{l_{1} F_{1} + l_{2} F_{2}}{F_{1} + F_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{l_{2} - l_{1}}{F_{2} - F_{1}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{l_{1} F_{2} - l_{2} F_{1}}{F_{2} - F_{1}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{l_{1} F_{1} - l_{2} F_{2}}{F_{2} - F_{1}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{l_{1} F_{2} - l_{2} F_{1}}{F_{2} - F_{1}}$
We have
$l_{1} - l = \frac{F_{1} l}{A Y}$
and
$l_{2} - l = \frac{F_{2} l}{A Y}$
Thus we get
$\frac{l_{1} - l}{F_{1}} = \frac{l_{2} - l}{F_{2}}$
or
$F_{2} l_{1} - F_{2} l = F_{1} l_{2} - F_{1} l$
or
$l = \frac{F_{2} l_{1} - F_{1} l_{2}}{F_{2} - F_{1}}$

Suggest Corrections

Similar questions

The length of a steel wire when stretched by a force $F_{1}$ is $l_{1}$ and when stretched by a force $F_{2}$ is $l_{2}$ .The unstretched length of the wire is

Q. The length of a metal wire is

l_{1}

when the tension in it is

F_{1}

and

l_{2}

when the tension is

F_{2}

. Then original length of the wire is:

Q. When the tension in a metal wire is

F_{1}

its length is

L_{1}

and then the tension in the wire is

F_{2}

the length is

L_{2}

. The natural length of the wire is

Q. A wire that obeys Hooke's law is of length

l_{1}

when it is in equilibrium under a tension

F_{1}

. Its length becomes

l_{2}

when the tension is increased of

F_{2}

. The energy stored in the wire during this process is

Q. The length of a uniform metal wire is observed to be

l_{1}

and

l_{2}

under the stretching forces

F_{1}

and

F_{2}

. The natural length of the wire is

Join BYJU'S Learning Program

The length of a metal wire is l1 when the tension in it is F1 and l2 when the tension in it is F2. The natural length of the wire is

The correct option is C l1F2−l2F1F2−F1We havel1−l=F1lAYandl2−l=F2lAYThus we getl1−lF1=l2−lF2orF2l1−F2l=F1l2−F1lorl=F2l1−F1l2F2−F1

The length of a metal wire is $l_{1}$ when the tension in it is $F_{1}$ and $l_{2}$ when the tension in it is $F_{2}$ . The natural length of the wire is