A man is rowing a boat of mass m with a constant velocity 'v0' in a river the contact area of boat is 'A' and coefficient of viscosity is η. The depth of river is 'D'. Assume that velocity gradient is constant. The force required to row the boat is
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a
ηAv02D
b
2ηAv0D
c
ηAv0D
d
3ηAv02D
answer is C.
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Detailed Solution
We can draw the free body diagram of boat Fext-Fv = maresAs boat moves with constant velocity ares = 0Fext = FvBut Fv = ηAdvdz, but dvdz = v0-0D = v0Dthen Fext = Fv = ηAv0Ddensity of water = 1g cm-3)