A uniform wire (Young's modulus 2 10^ 11 , Nm^ -2 ) is subjected … - Vidyadip

MCQ

A uniform wire (Young's modulus $2 \times 10^{11}\, Nm^{-2}$ ) is subjected to longitudinal tensile stress of $5 \times 10^7\,Nm^{-2}$ . If the over all volume change in the wire is $0.02\%,$ the fractional decrease in the radius of the wire is close to

A
$1.0\times 10^{-4}$
B
$1.5\times 10^{-4}$
✓
$0.25\times 10^{-4}$
D
$5\times 10^{-4}$

✓

Answer

Correct option: C.

$0.25\times 10^{-4}$

c
$Given,\,y = 2 \times {10^{11}}N{m^{ - 2}}$

$Stress\left( {\frac{F}{A}} \right) = 5 \times {10^7}N{m^{ - 2}}$

$\Delta V = 0.02\% = 2 \times {10^{ - 4}}{m^3}$

$\frac{{\Delta r}}{r} = ?$

$\gamma = \frac{{stress}}{{strain}} \Rightarrow strain\left( {\frac{{\Delta \ell }}{{{\ell _0}}}} \right) = \frac{\gamma }{{stress}}\,\,...\left( i \right)$

$\Delta V = 2\pi {\ell _0}\Delta r - \pi {r^2}\Delta \ell $ $...\left( {ii} \right)$

From eqns $(i)$ and $(ii)$ putting the value of

$\Delta \ell ,{\ell _0}\,and\,\Delta V\,and\,solving\,we\,get$

$\frac{{\Delta r}}{r} = 0.25 \times {10^{ - 4}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 8. mechanical properties of solids→8. mechanical properties of solids — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The radius of a disc is $1.2\; cm$. Its area according to the concept of significant figures will be given by

Two bodies are held separated by $9.8\,m$ vertically one above the other. They are released simultaneously to fall freely under gravity. After $2\,s$, the relative distance between them is $............\,m$

If ${C_V} = 4.96cal/mole\, K$, then increase in internalenergy when temperature of $2$ moles of this gas is increased from $340 K$ to $342 K$ ....... $cal$

Which of the following pairs represent units of the same physical quantity?

The relation between time $t$ and distance $x$ for a moving body is given as $t=m x^{2}+n x$, where ${m}$ and ${n}$ are constants. The retardation of the motion is -

(Where $v$ stands for velocity)

A solid body rotates about a fixed axis such that its angular velocity depends on $\theta$ as $\omega=k \theta^{-1}$ where $k$ is a positive constants. At $t=0, \theta=0$, then time dependence of $\theta$ is given as ..........

A bomb is projected upwards. At topmost point it explodes in three identical fragments. First fragment comes to ground in $10\ sec$. and others in $20\ sec$ each. Then the height reached by the original bomb is.........$m$

Graph between power and time is given below. Then which of the following option is correct for work done by force [from $t = 0$ to time $t$]

The efficiency of an engine will be maximum when it works:

Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^{\circ}, 30^{\circ}, 45^{\circ}$ and $60^{\circ}$ with the horizontals respectively. The body having shortest range is