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Q.

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  tan⁡θ=x10 ……..(1)This angle should be angle of repose. or  tan⁡θ=μ=12  ……(2)From Eqs. (1) and (2),       x10=12 or x=5m∴ y=x220=2520=1.25m
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