A rod of length 10 m initially at 100 K is heated till its temperature increases to 200 K . If coefficient of linear expansion of the rod is given by α=α0Tx , where α0=2×10−11 S.I. unit, x is distance measured from one end of the rod (in m ) & T is temperature in kelvin. Find the change in length (inμm ) of the rod.

dl=(α0TdT)∫0Lxdx=α0L22TdTΔl=α0L22∫100200TdtΔl=10−11×10×32×104=1.5μm

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A rod of length $\sqrt{10}$ m initially at 100 K is heated till its temperature increases to 200 K . If coefficient of linear expansion of the rod is given by $α = α_{0} T x$ , where $α_{0} = 2 \times 10^{- 11}$ S.I. unit, x is distance measured from one end of the rod (in m ) & T is temperature in kelvin. Find the change in length (in $μ m$ ) of the rod.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 1.5.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} d l = (α_{0} T d T) {\int^{}}_{0}^{L} x d x = \frac{α_{0} L^{2}}{2} T d T \\ Δ l = \frac{α_{0} L^{2}}{2} {\int^{}}_{100}^{200} T d t \\ Δ l = 10^{- 11} \times 10 \times \frac{3}{2} \times 10^{4} = 1.5 μ m \end{array}$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!