KVPY SA Exam 05-Nov-2017 Question Paper

Question : 70 of 80

Marks: +1, -0

Stoke’s law states that the viscous drag force F experienced by a sphere of radius a, moving with a speed Vthrough a fluid with coefficient of viscosity η, is given by F = 6πnaν. If this fluid is flowing through a cylindricalpipe of radius r, length l and a pressure difference of P across its two ends, then the volume of water V whichflows through the pipe in time t can be written as

V/t=k(P/l)^a η^br^c

, where k is a dimensional constant.Correct values of a, b and c are

a = 1, b = –1, c = 4
a = –1, b = 1, c = 4
a = 2, b = –1, c = 3
a = 1, b = –2, c = –4

Validate

Solution:

V/t=k(P/l)^a .η^b.γ^c

[r] = L; [l] = L

[P] = ML^{–1}T^{–2}; [η] = ML^{–1}T^{–1}

[V] = L^3

[t] = T
By calculation
a = 1; b = –1; c = 4

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