Define terminal velocity. Show that the terminal velocity upsilon of a sphere of radius r, density rho falling vertically through a viscous fluid of density sigma and coefficient of viscosity eta is given by upsilon = 2 / 9 ((rho - sigma)r^2 g) / eta Use this formula to explain the observed rise of air bubbles in a liquid.

What do you understand by resistance of a conductor ? Define its SI unit. Show that resistance of a conductor is given by R=(ml)/(n e^(2) tau A) , where the symbols have their usual meanings.

Find the dimensional formulae of the following quantities: a. the universal constant of gravitation G, b. the surface tension S, c. the thermal conductivity k and d. the coeficient of viscosity eta . Some equation involving these quantities are F=(Gm_1m_2)/r^2, S= (rho g r h)/2, Q=k(A(theta_2-theta_1)t)/d and F=- rho A (v_2-v_1)/(x_2-x_1) where the symbols have their usual meanings.

Ac cording to Bernoulli's theorem for the streamline flow of an ideal liquid, the sum of pressure energy/mass, kinetic energy/mass and potential energy /mass remains constant at every cross section, throughout the liquid flow. i.e., (P)/(rho) + (1)/(2)upsilon^2 + gh = cosntant, where the symbols have their usual meaning. Note that an ideal liquied is the one, which is perfectly incompressible, irrotational and non visous. Read the above passage and answer the following question ? (i) At what speed will the velocity head of a stream of water be equal to 40 cm ? (ii) What is the implication of Bernoulli's theorem in day to day life ?

A vertical steel rod has radius a. The rod has a coat of a liquid film on it. The liquid slides under gravity. It was found that the speed of liquid layer at radius r is given by v=(rhogb^(2))/(2eta)ln((r)/(a))-(rhog)/(4eta)(r^(2)-a^(2)) Where b is the outer radius of liquid film, eta is coefficient of viscosity and rho is density of the liquid. (i) Calculate the force on unit length of the rod due to the viscous liquid? (ii) Set up the integral to calculate the volume flow rate of the liquid down the rod. [you may not evaluate the integral]

A wire of density rho and Youngs modulus Y is streched between two rigid supports separated by a distance L and is under a tension T. Derive an expression for its frequency in the fundamental mode. Hence show that n=(1)/(2L)sqrt((Yl)/(rhoL)) , where the symbols have their usual meanings.

A solid sphere, of radius R acquires a terminal velocity v_(1) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity h. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v_(2) , when falling through the same fluid, the ratio (v_(1)//v_(2)) equal 9/x . Find the value of x.

Find the dimensional formulae of following quantities: (a) The surface tension S, (b) The thermal conductivity k and (c) The coefficient of viscosity eta . Some equation involving these quantities are S=(rho g r h)/(2) " " Q=k(A(theta_(2)-theta_(1))t)/(d) and " " F=-etaA(v_(2)-v_(1))/(x_(2)-x_(1)) , where the symbols have their usual meanings. ( rho -density, g- acceleration due to gravity , r-radius,h-height, A-area, theta_(1)&theta_(2) - temperatures, t-time, d-thickness, v_(1)&v_(2) -velocities, x_(1)& x_(2) - positions.)