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1. Volume of a liquid flowing per second,V is proportional to i) the coefficient of viscosity, n ii) the radius of the pipe, a iii) the pressure gradient, g V ∝ nˣaʸgᶻ V = knˣaʸgᶻ where k is a constant of propotionality. Using dimentional analysis, obtain the values of the constants x, y and z,hence the explict expression of V 2. The velocity, v of a wave setup in a stretched string by plucking it can be given in terms of (i) the tension, F of the string (ii) the mass, M of the string and (iii) the length, L of the string v ∝ FˣLʸmᶻ V = KFˣLʸmᶻ :use dimensional analysis to obtain the values of x, y and z. 3. The period, T of oscillation of a loaded spiral spring is found to depend on: (i) loaded mass,m and the effective mass of the spring mₑ (ii) the elastic constant K of the spring and (iii) the acceleration due to gravity, g I.e T∝(m+mₑ)ˣKʸgᶻ or T=a(m+mₑ)ˣKʸgᶻ. where a is the dimensionless constant. : Using dimensional analysis express T
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