Area Bounded:

Consider the isotherms drawn in the F(E) vs E graph.

Find the area bounded by the isotherm at T=0K and the E-axis.

Notes:
1)'E' means energy.
2)'T' is temperature, 'k' is your Boltzmann constant.
3)F(E) is the equation for the Fermi-Dirac statistics.
4)The above 3 are insignificant for the problem.

The horizontal bottom of a wide vessel with an ideal fluid has a round orifice of radius R1 over which a round closed cylinder is mounted, whose radius R2>R1. The clearance between the cylinder and the bottom of the vessel is very small, the fluid density is p. Find the static pressure of the fluid in the clearance as a function of the distance r from the axis of the orifice (and the cylinder), if the height of the fluid is equal to h.

Error Analysis contd..

Rules:

1)'D' is the distance b/w the virtual sources and the eyepiece, measured with a scale of least count 1mm.
Procedure: The virtual sources are at '0' on the optical bench (no zero error). The coordinate of the eyepiece is taken.

2)The fringe width and 'd1' and 'd2' (displacement method values) are measured with a micrometer screw of LC .01mm.
Procedure:: The cross-hair is set at a good- dark fringe (or at the image of a virtual source). Then it is moved to the 25th fringe (or to the image of the other virtual source). The difference between the 2 readings is taken.

Find the wavelength of the light used. What light is this?

Fresnel Biprism:

This is the experimental setup that we'll be analyzing for error. (but lets do the theory first.)

1)Why are we using the bi-prism at all?? 2 marks
2)Why should the angle of the bi-prism be small?? 2 marks
3)Suggest a method for measuring the distance between the 2 virtual sources formed by the bi-prism. 4 marks.

In the diagram, I've also shown the view from the eyepiece. Also notice the red cross-hair. It can be moved by turning the screw of a micrometer, hence allowing us to measure the distance between the fringes!!

Hint: you'd like to use the eyepiece for Q3.

Mood Swings and Error Analysis:

The next question will be on error analysis. This is your one chance to try out a well-framed problem in the topic.

It will be lengthy, (and a bit irritating also). But remember: the one thing that matters is error analysis is the "Correct Answer".

Constraints:

These are 2 rods free to rotate in a vertical plane. The upper rod is rotated with an angular velocity 'w'. What is the angular velocity of the lower rod if AB=AC.

Double Star

Consider the double star:

It consists of two planets of mass M and m separated by distance 'R'. They revolve around their common center of mass.

What is the time period of revolution for 'm'? For 'M'?

Explain the observation.

Heat

A constant electric current flows along a uniform wire with cross-sectional radius ‘R’ and heat conductivity coefficient ‘K’. A unit volume of the wire generates a thermal power ‘W’. Find the temperature distribution across the wire provided the steady-state temperature at the wire surface is equal to T.

Lessons in Vectors:

A point electric dipole with a moment 'p' is placed in the external uniform electric field whose strength equals 'E', with p parallel to E. In this case one of the equi-potential surfaces enclosing the dipole forms a sphere. Find the volume of this sphere.

All about squares:

What is the number of squares that can be formed by joining points in a 10*20 square grid??

The figure shows a 6*4 grid and various possible squares in it.

Snipping tool and copyrights:

A small coil C with N = 200 turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet. The cross-sectional area of the coil
S=1.0cm^2, the length of the arm OA of the balance beam is L=30 cm.

When there is no current in the coil the balance is in equilibrium. On passing a current I = 22 mA through the coil the equilibrium is restored by putting the additional counterweight of mass M = 60 mg on the balance pan. Find the magnetic induction at the spot where the coil is. located.

Ans: .4 T..