(ii) In an experiment to determine the acceleration due to gravity (g), a small ball bearing is timed while falling freely from rest through a measured vertical height. The following data were obtained: vertical height h=(600+-+1) mm, time taken t ms. Calculate the numerical value of g from the experimental data, clearly specify the errors.
(b) A small mass of 0.15kg is suspended from a fixed point by a thread of a fixed length. The mass is given a push so that it moves along a circular path of radius 1.82m in a horizontal plane at a steady speed, taking 18.0s to make 10 complete revolutions. Calculate:
(i) The speed of the small mass; (ii) the centripetal acceleration; (iii) the tension in the thread.
4. (a) (i) State Surface tension in terms of energy.
(ii) The surface tension of water at 200C is 7.28 x 10-2 Nm-l . The vapour pressure of water at this temperature is 2.33 x 103 Pa . Determine the radius of smallest spherical water droplets which it can form without evaporating.
(b) A circular ring of thin wire 3cm in radius is suspended with its plane horizontal by a thread passing through the 10cm mark of a metre rule pivoted at its centre and is balanced by 8g weight suspended at the 80cm mark. When the ring is just brought in contact with the surface of a liquid, the 8g weight has to be moved to the 90cm mark to just detach the ring from the liquid. Find the surface tension of the liquid (assume zero angle of contact).
(ii) In a special type thermometer a fixed mass of a gas has a volume of 100cm3 at a pressure of 81.6cmHg at the ice point and volume of 124cm3 and pressure of 90cmHg at steam point. Determine the temperature if its volume is 120cm3 and pressure of 85cmHg.
(iii) What value does the scale of this thermometer give for absolute zero?
(ii) A solid copper sphere cools at the rate of2.80C/min when its temperature is 1270C. At what rate will a solid copper sphere of twice the radius cool when its temperature is 227C C? In both cases the surroundings are kept at 27oc and conditions are such that Stefan's law may be applied.
(b) (i) A glass disc of radius 5cm and uniform thickness of 2mm had one of its sides maintained at 1000C while a copper block in good thermal contact with this side was found to be 700C. The copper block weighs 0.75kg. The cooling of copper was studied over a range of temperature and the rate of cooling at 700C was found to be 16.5K/ min. Determine the thermal conductivity of glass.
(ii) A cylindrical element of 1kW electric fire is 30cm long and 1.0cm in diameter. If the temperature of the surroundings is 20 0C, estimate the working temperature of the element.
(b) A heating coil is made of a nichrome wire which will operate on a 12V supply and will have a power of 36W when immersed in water at 373K. The wire available has a cross-sectional area of 10mm2 . What length of the wire will be required?
(b) (i) Show that the unit of CR (time constant) is seconds and prove that for a discharging capacitor it is the time taken for the charge to fall by 37%.
(ii) The variable radio capacitor can be charged from 50pF to 950pF by turning the dial from 0 0 to 1800. With the dial at 1800, the capacitor is connected to a 400V battery. After charging the capacitor is disconnected from the battery and the dial is turned to 0 0. What is the charge on the capacitor? What is the p.d. across the capacitor when the dial reads 0 0 and the work done required to turn the dial to 0 0? (Neglect frictional effect).
13. (a) (i) Without giving any experimental or theoretical detail explain how the results of Millikan's experiment led to the idea that charge comes in 'packets', the size of the smallest packet being carried by an electron.
(ii) In the form of Millikan's experiment, an oil drop was observed to fall with a constant velocity of 2.5 10-4 ms- in the absence of an electric field. When a p.d of 1000V was applied between the plates 10mm apart, the drop remained stationary between them. If the density of oil is 9 x 102 kgm-3 density of air is 1.2kgm-3 and viscosity of air is 1.8 10-5Nsm-2. Calculate the radius of the oil drop and the number of electric charges it carries.