Download App

Model Paper 8 — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsModel Paper 83 Marks
Question
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57^{\circ} C$ is drunk. You can take body (tooth) temperature to be $37^{\circ} C$ and $\alpha=1.7 \times 10^{-5} / K$. Bulk modulus for copper $=140$ $\times 10^9 N / m ^2$.
✓

Answer

First of all, the stress on the object(tooth) developed over here is dependent on bulk modulus of the material and the temperature difference. That's the stress is called a thermal stress over here.
Now, change in temperature $\Delta T=57-37=20^{\circ} C =20 K$ (since temperature difference is same here in both the scales)
Coefficient of linear expansion $\alpha$ of (tooth) body $=1.7 \times 10^{-5} K^{-1}$
Cubical expansion $\gamma=3 \alpha=3 \times 1.7 \times 10^{-5}=5.1 \times 10^{-5} K^{-1},\left[ As , \alpha=\frac{\gamma}{3}\right]$
Let the volume of the cavity be V and its volume increased by $\Delta V$ due to increase in temperature $\Delta T$.
Then from the defination of coefficient of volume expansion,
$
\begin{aligned}
& \Delta V=\gamma V \cdot \Delta T \\
& \Rightarrow \frac{\Delta V}{V}=\gamma \Delta T
\end{aligned}
$
Thermal stress produced $=$ Bulk modulus $\times$ Volume strain
$
=B \times \frac{\Delta V}{V}=B \times \gamma \times \Delta T
$
Hence, thermal stress $=140 \times 10^9 \times 5.1 \times 10^{-5} \times 20=14280 \times 10^4 N / m ^2$, as bulk modulus $=140 \times 10^9 N / m ^2($ given $)$
$
=1.428 \times 10^8 Nm^{-2}
$
This stress is about $10^3$ times of atmospheric pressure i.e., $1.013 \times 10^5 Nm ^{-2}$.

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 "3 Marks Question" from Model Paper 8→Model Paper 8 — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The intensity of sound in a normal conversation at home is about $3 \times 10^{-6} Wm ^{-2}$ and the frequency of normal human voice is about $1000 Hz$ . Find the amplitude of waves, assuming that the air is at standard conditions.
→
Calculate the acceleration due to gravity at the surface of Mars if its diameter is $6760km$ and mass one tenth that of the earth. The diameter of earth is $12742km$ and acceleration due to gravity on the earth is $9.8m/ s^2$.
→
A steel wire of original length 1m and cross-sectional area $4.00mm^2$ is clamped at the two ends so that it lies horizontally and without tension. If a load of $2.16kg$ is suspended from the middle point of the wire, what would be its vertical depression? Y of the steel = $2.0 \times 10^{11}N/m^2$ Take $g = 10m/s^2$​​​​​​​.
→
A string is wrapped on a wheel of moment of inertia $0.20kg-m^2$ and radius 10cm and goes through a light pulley to support a block of mass $2.0kg$ as shown in figure. Find the acceleration of the block.
→
A liquid is in streamlined flow through a tube of non uniform cross-section. Prove that sum of its kinetic energy, pressure energy and potential energy per unit volume remain constant.
→
The ends of a metre stick a.re maintained at $100^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$. One end of a rod is maintained at $25^{\circ} \mathrm{C}$. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?
→
A spherical volume contains a uniformly distributed charge of density $2.0 \times 10^{-4}Cm^{-3}$. Find the electric field at a point inside the volume at a distance $4.0cm$ from the centre.
→
How to find displacement from velocity-time graph? Explain.
→
The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes $3.0$ billion years to reach us?
→
A particle moves in a straight line such that its displacement at any time is given by $s^2 = t^2 +1$. Find
  1. Velocity.
  2. Acceleration as a function of $s$.
→