CameraIcon

SearchIcon

MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Thermal Expansion

A uniform rod...

Question

A uniform rod of length L, cress-sectional area A and Young's modulus Y is stretched by applying two force $F_{1}$ and $F_{2}$ as shown in figure. The elongation in the rod will be ( $F_{1}$ > $F_{2}$ )

A

\frac{(F_{1} + F_{2}) L}{A Y}

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

B

\frac{(F_{1} - F_{2}) L}{2 A Y}

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

C

\frac{(F_{1} + F_{2}) L}{2 A Y}

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

D

\frac{F_{1} L}{2 A Y}

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

Open in App

Solution

The correct option is C $\frac{(F_{1} + F_{2}) L}{2 A Y}$
$\begin{matrix} Abplying NLM: 2 law, F_{1} - T = ρ A X . a T - F_{2} = P A \cdot (L - x) a \end{matrix}$
$\frac{(F_{1} - T)}{T - F_{2}} = \frac{x}{L - x}$
$T = F_{1} - \frac{x (F_{1} - F_{2})}{L}$
$Elongation Δ l = \int_{0}^{L} \frac{T d x}{A y} f_{0}^{L} \frac{[F_{1} - \frac{x}{L} (F_{1} - F_{2})] d x}{A Y} = \frac{(F_{1} + F_{2})}{2 A Y}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A uniform rod of length L, cross-sectional area A and Young's Y is stretched by applying two force

F_{1}

F_{2}

as shown in figure. The elongation in the rod will be

(F_{1} > F_{2})

Q. A homogeneous rod of length

L

is acted upon by two forces

F_{1}

F_{2}

applied to its ends and directed opposite to each other. If

F_{2} > F_{1}

, then with what force

F

will the rod be stretched at the across section at a distance

l

from the end where

F_{1}

Q. Tension in rod of length

L

M

y

F_{1}

when the rod is acted on by two unequal forces

F_{1}

F_{2}

F_{2} < F_{1}

) at its ends is :-

Q. A rod of length 'L' and mass 'M' is acted on by two unequal forces

F_{1}

F_{2}

F_{1}

) as shown in the following figure. The Tension in the rod at a distance 'y' from the end 'A' is given by :

Q. A homogeneous rod of length

L

is acted upon by two forces

F_{1}

F_{2}

applied to its ends and directed opposite to each other. With what force

F

will the rod be stretched a the crosssection at a distance

l

from the end where force

F_{1}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Thermal Expansion

PHYSICS

Watch in App

explore_more_icon

Explore more

Thermal Expansion

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon