(c) (i) The frequency 'f' of vibration of a stretched string depends on the tension 'F', the length 'l' and the mass per unit length g of the string. Derive the formula relating the physical quantities by the method of dimensions.
(ii) Use dimensional analysis to prove the correctness of the where p
= density of the earth, g = acceleration due to gravity, R radius of the earth and G = gravitational constant.
(b) An object of mass 1 kg is attached to the lower end of a string 1 m long whose upper end is fixed and made to rotate in a horizontal circle of radius 0.6 m. If the circular speed of the mass is constant, find the:
(c) The value of the property X of a certain substance is given by:
X = X + 0.50 + 2 x 10-4 Ø2, where Ø is the temperature in degree celsius. What would be the Celsius the temperature defined by the property X which corresponds to a temperature of 50 oc on this gas thermometer scale?
(C) A potential difference of 4V is connected to a uniform resistance wire of length 3.0 m and cross-sectional area 9 x 10-9, when a current of 0.2 A is flowing in the wire. Find the; (i) Resistivity of the wire