Question #70714

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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