(b) Using the method of dimensions, indicate which of the following equations aredimensionally correct and which are not, given that, f = frequency, y = surface tension, p = density, r = radius and k = dimensionless constant.
(b)A clean open ended glass U-tube has vertical limbs one of which has a uniform internal diameter of 4.0 mm and the other of 20.0 mm. Mercury is poured into the tube; and observed that the height of mercury column in the two limbs is different.
(b) (i) A person sitting on a bench on a calm hot summer day is aware of a cool breeze blowing from the sea. Briefly explain why there is a natural convection.
(ii) A Nichrome-constantan thermocouple gives about 70 VIV for each IOC difference in temperature between the junctions. If 100 such thermocouples are made into a thermopile, what voltage is produced when the junctions are at 200C and 2400C?
(c)A black body of temperature 0 is placed in a blackened enclosure maintained at a temperature of IOOC. When its temperature rises to 300C the net rate of loss of energy from the body was found to be 10 watts. Find the power generated by the body at 500C if the energy exchange takes place solely by the process of forced convection.
(b)(i) Write down three laws governing the black body radiation.
(ii) A cup of tea kept in a room with a temperature of 220C cools from 660C to 630C in 1 minute. How long will the same cup of tea take to cool from the temperature of 430C to 400C under the same condition?
(c)A small speaker emitting a note of frequency 250Hz is placed over the open upper end of avertical tube which is full of water. When the water is gradually run out of the tube the air column resonates. If the initial and final position of water surface below the top is 0.31m and 0.998m respectively, calculate the speed of sound in air and the end-correction of the tube.
(b)In an intrinsic semiconductor, the energy gap Eg is 1.2 eV, and its hole mobility is very much smaller than electron mobility which is independent of temperature. Assuming that the temperature dependence of intrinsic carrier concentration, n. is expressed as:
(i)What is the ratio between conductivity at 600K and that at 300K? (ii) Comment on the result obtained in (b) (i).
(ii) A radioactive source in the form of metallic sphere of radius 1.0 cm emits ß-particles at the rate of 5.0 x 1010particles per second. If the source is electrically insulated, how long will it take for its electric potential to be raised by 2.0 Volts? (Assuming that 40% of the emitted ß-particles escape the source).
(b) (i) Draw a schematic diagram of an electron microscope showing its main parts.
(ii)Give the order of resolution of electron microscope in (b) (i) above.
(c) (i) Briefly explain why Cathode Ray Oscilloscope (C.R.O) is said to be an excellent instrument for measuring the e.m.f.
(ii) An electron gun fires electrons at the screen of a TV tube. The electrons start from rest and are accelerated through a potential difference of 30kV. What is the speed of impact of electrons on the screen of the picture tube?
(b)An oscilloscope is used to measure the waveform across a 5000 resistor in an a.c. circuit as shown in Figure 2. Given that the time base of the oscilloscope is set at 5mscm-1, its Y—gain at 0.5Vcm1and the grid has squares of 1.0cm, calculate: