GATE 2018 ME (ME1) – Question 53
A 2 kg block slides steadily down a vertical wall, lubricated by an oil film 0.15 mm thick over area 0.04 m². Film velocity varies linearly as shown. Oil dynamic viscosity is $7\times10^{-3}$ Pa s; g = 10 m/s². Neglect oil weight. Terminal speed, to one decimal, is ______ m/s.
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Show answer and explanation
Correct answer: 10.6 to 10.8
Explanation
At terminal speed, weight balances viscous drag: $mg=\mu VA/h$. Hence $V=mgh/(\mu A)=2(10)(0.00015)/(0.007\times0.04)=10.7143$ m/s, or 10.7 m/s.