A parabolic bowl with its bottom at origin has the shape y=x2/20. Here x and y are in metres. The maximum height at which a small mass m can be placed on the bowl without slipping (coefficient of static friction is 0.5) is
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a
2.5 m
b
1.25 m
c
1.0 m
d
4.0 m
answer is B.
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Detailed Solution
dydx=x10 or tanθ=x10 ……..(1)This angle should be angle of repose. or tanθ=μ=12 ……(2)From Eqs. (1) and (2), x10=12 or x=5m∴ y=x220=2520=1.25m