Question
Define thermal conductivity and write its practical applications.

Answer

SELF

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In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by $\frac{\text{Y}\pi\text{r}^4}{4\text{R}}.$ Y is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.
A neutron initially at rest, decays into a proton, an electron and an antineutrino. The ejected electron has a momentum of 1.4 × 10-26kg-m/s and the antineutrino 6.4 × 10-27kg-m/s. Find the recoil speed of the proton:
  1. If the electron and the antineutrino are ejected along the same direction.
  2. If they are ejected along perpendicular directions. Mass of the proton = 1.67 × 10-27kg.
The length of a second’s pendulum on the surface of Earth is 1m. What will be the length of a second’s pendulum on the moon?
A convex lens has a focal length of 10cm. Find the location and nature of the image if a point object is placed on the principal axis at a distance of:
  1. 9.8cm
  2. 10.2cm from the lens.
If 28 × 1023 molecules of a gas strike a surface of area 14cm2 normally per second with velocity of 500 ms-1 and rebound in the opposite direction with the same speed find the pressure exerted by the gas on the surface if mass of each molecule is 5 × 10-23 g.
Mention examples of motion of center of mass.
A great physicist of this century (PAM Dirac) loved playing with the numerical values of fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics me, mp and the gravitational constant G, he could arrive at a number with the dimension of time.
Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion yr).
From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?
A uniform wheel of radius R is set into rotation about its axis at an angular speed $\omega.$ This rotating wheel is now placed on a rough horizontal surface with its axis horizontal. Because of friction at the contact, the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling on the surface. Find the linear speed of the wheel after it starts pure rolling.
  1. What is beat phenomenon?
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A whistle revolve in a circle with angular velocity of o = 20 rad s-1. If the frequency of the sound is 385Hz and speed is 340ms-1, than find the frequency heard by the observer when the whistle is at B.

Derive an expression for the moment of inertia of a thin uniform rod about an axis passing through its one end and perpendicular to its length. Also determine the radius of gyration about the same axis.