Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics-

General

Easy

Question

If the ratio of lengths, radii and Young’s modulus of steel and brass wires shown in the figure are $a comma blank b$ and $c$ , respectively. The ratio between the increase in lengths of brass and steel wires would be

$\frac{b^{2} a}{2 c}$
$\frac{b c}{2 a^{2}}$
$\frac{b a^{2}}{2 c}$
$\frac{a}{2 b^{2} c}$

The correct answer is: $fraction numerator a over denominator 2 b to the power of 2 end exponent c end fraction$

Given, $fraction numerator l subscript 1 end subscript over denominator l subscript 2 end subscript end fraction equals a comma fraction numerator r subscript 1 end subscript over denominator r subscript 2 end subscript end fraction equals b comma fraction numerator Y subscript 1 end subscript over denominator Y subscript 2 end subscript end fraction equals c$

Let Young’s modulus of steel be $Y subscript 1 end subscript$ , and that of brass be $Y subscript 2 end subscript$
$therefore Y subscript 1 end subscript equals fraction numerator F subscript 1 end subscript l subscript 1 end subscript over denominator A subscript 1 end subscript increment l subscript 1 end subscript end fraction$ (i)
and $Y subscript 2 end subscript equals fraction numerator F subscript 2 end subscript l subscript 2 end subscript over denominator A subscript 2 end subscript increment l subscript 2 end subscript end fraction$ (ii)
Dividing Equation (i) by Equation (ii), we get
$fraction numerator Y subscript 1 end subscript over denominator Y subscript 2 end subscript end fraction equals fraction numerator F subscript 1 end subscript. A subscript 2 end subscript. l subscript 1 end subscript. increment l subscript 2 end subscript over denominator F subscript 2 end subscript. A subscript 1 end subscript. l subscript 2 end subscript. increment l subscript 1 end subscript end fraction$ (iii)
Force on steel wire from free body diagram
$T equals F subscript 1 end subscript equals left parenthesis 2 g right parenthesis$ Newton
Force on brass wire from free body diagram
$F subscript 2 end subscript equals T subscript 1 end subscript superscript ´ ´ end superscript equals T plus 2 g equals 4 g$ Newton
Now, putting the value of $F subscript 1 end subscript comma F subscript 2 end subscript comma$ in Equation (iii), we get
$fraction numerator Y subscript 1 end subscript over denominator Y subscript 2 end subscript end fraction equals open parentheses fraction numerator 2 g over denominator 4 g end fraction close parentheses. open parentheses fraction numerator pi r subscript 2 end subscript superscript 2 end superscript over denominator pi r subscript 1 end subscript superscript 2 end superscript end fraction close parentheses. open square brackets fraction numerator l subscript 1 end subscript over denominator l subscript 2 end subscript end fraction close square brackets. open parentheses fraction numerator increment l subscript 2 end subscript over denominator increment l subscript 1 end subscript end fraction close parentheses equals fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator 1 over denominator b subscript 2 end subscript end fraction close parentheses. a open parentheses fraction numerator increment l subscript 2 end subscript over denominator increment l subscript 1 end subscript end fraction close parentheses$

Related Questions to study

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.