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tudinal wave? What is being propagated in the case of light, heat, and sound waves and to which class, transverse or longitudinal, does each belong?

11. Define: mechanical equivalent of heat, calorie, specific heat, latent heat of vaporization, absolute temperature, coeffiicient of expansion. Mention the unique thermal properties of water and explain why these are of extreme importance.

12. A current of five amepres flows in a coil of wire, of eighty ohms resistance, for one hour, so that the heat developed in the coil is entirely given up to a liquid surrounding the coil, both being within a calorimeter. If the specific heat of the liquid is 0.85, the weight of the liquid 2000 gms., and the water equivalent of calorimeter parts in contact with the liquid 40, what will be the rise in temperature of the liquid?

SENIOR PHYSICS.

A. Dynamics.

(Any three questions).

1. (a) Show that the moment of inertia of a body about an axis is given by Emr2 where r is the distance of a small part of the body from the axis in question, m being the mass of this part.

(b) Justify the use of the term moment of inertia as describing this quantity.

(c) Establish the relation L-Ia where L is the couple acting on the body, I is the moment of inertia about the axis of L, and a is the resulting angular acceleration.

2. A cylinder (radius 15 cm., mass 50 kilograms) turns on a horizontal axis about which its radius of gyration is 12 cm. A rope is wound on the cylinder and the free end is attached to a bucket of mass 5 kilograms. The bucket descends 6 metres to the ground. Neglecting axle friction and the mass and weight of the rope, find:

(a) The angular momentum of the cylinder 2 seconds after the motion begins.

(b) The kinetic energy of the bucket as it strikes the ground, and

(c) The tension of the rope during the motion.

bar to a

3. A uniform bar 100 x 5 x 5 cm. and density 2 is hinged to the wall at one end and is supported in a horizontal position by a string that runs vertically from the free end of the point on the ceiling 2 metres above. The moment of inertia of a rectangular bar about its centre of gravity is given by I=1/M (+62). The free end of the bar is given a small lateral displacement. Show that the subsequent motion is simple harmonic, and express the period as a complex fraction involving the dimensions of the system.

4. A four-wheeled warehouse truck has axles 4 feet apart. The centre of gravity of the loaded truck is 1 foot in front of the rear axle and is 2 feet above the level of the axles. The truck is set in motion along a level floor by a horizontal force acting 3 feet above the level of the axles and for a short time an acceleration of 0.6 feet per second is produced. Taking the mass of truck and load as 1000 lbs. and friction as 20 pounds-weight per ton, find the value of the applied force and of the reaction at each axle while the acceleration has the value 0.6.

B. Heat and Light.

(Any three questions).

5. If the coefficients of cubical expansion of glass and mercury are .000025 and .00018 respectively, what fraction of the entire volume of a glass vessel should be filled with mercury in order that the volume of the empty part should remain constant when glass and mercury are heated to the same temperature?

6. A slice of Iceland Spar is cut perpendicular to the optic axis and placed between crossed Nicols, using parallel white light. Explain what is seen. If the light falling on the crystal slice is convergent, what will be seen? Explain.

7. Monochromatic light from a narrow slit falls on two parallel slits 0.2 mm. apart. The interference bands are seen on a screen 100 cm. away and are found to be 2.95 mm. apart. What is the wave-length of the light?

8. Discuss briefly the following topics: Triple point, Specific heats of a gas, Boiling point of water, Huyghen's principle, Undulatory theory of light, Spherical and chromatic aberration, Diffraction grating.

C. Electricity and Magnetism.

(Any three questions).

9. Show that a body of capacity C raised to a potential V

has an electrical potential energy measured by ¿CV2.

10. Describe the application of two distinct electrical principles to the measurement of temperature.

11. Four wires of 3 ohms each are connected to form a square ABCD. The zinc plate of a cell (E.M.F. 2 volts, internal resistance 1 ohm) is joined to the point A by a wire of 2 ohms resistance and a similar wire connects the copper plate of this cell to the point B. A second cell (E.M.F. 4 volts, internal resistance 2 ohms) has its zinc plate connected to C and its copper plate to D by wires of 3 ohms each. Show by a diagram the directions of the currents in each of the wires of the net and calculate to one per cent. the magnitudes of these currents in amperes.

12. A rod 2 metres long rolls slowly off a shelf and falls 3 metres to the ground. During its fall the rod is always horizontal and normal to the geographical meridian. Express as a complex fraction of the data the potential difference from end to end as it strikes the ground. Take total magnetic intensity 0.62, declination 10° west of North, dip 70°.

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