Project ForgeA solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall. A thin oil film of thickness h=0.15 mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oil film is 0.04 m². The velocity distribution within the oil film gap is linear. Dynamic viscosity of oil = 7×10⁻³ Pa·s, acceleration due to gravity = 10 m/s². Neglect weight of the oil. The terminal velocity V (in m/s) of the block is _________ (correct to one decimal place).
Explanation
At terminal velocity, the block's weight is balanced by the viscous shear force from the linear (Couette) oil-film profile: mg = μ(V/h)A. V = mgh/(μA) = (2×10×0.00015)/(0.007×0.04) = 0.003/0.00028 ≈ 10.7 m/s.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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