A rod of length 20 cm is made of metal. It expands by 0.075cm when its temperature is raised from 0°C to 100°C. Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature. The portion made of metal A has the length

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

10 cm

15 cm

18 cm

20 cm

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\Delta L = {L_0}\,\alpha \Delta \theta$
Rod A : 0.075 = 20 x $\alpha$ _A x 100 $\Rightarrow$ ${\alpha _A} = \frac{{75}}{2} \times {10^{ - 6}}/^\circ C$
rod B : 0.045 = 20 x $\alpha$ _B x 100 $\Rightarrow$ ${\alpha _B} = \frac{{45}}{2} \times {10^{ - 6}}/^\circ C$
For composite rod : x cm of A and (20 – x) cm of B we have

Question Image
0.060 = x $\alpha$ _A x 100 + (20 – x) $\alpha$ _B x 100
$= x\,\left[ {\frac{{75}}{2} \times {{10}^{ - 6}} \times 100 + (20 - x) \times \frac{{45}}{2} \times {{10}^{ - 6}} \times 100} \right]$
On solving we get x = 10 cm