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Question

A railway carriage box has its geometric centre (i.e we will assume the force due to gravity to act at this point) at a height of 1 m above the rails, which are 1.5 m apart. The maximum safe speed at which it could travel round an unbanked curve of radius 100 m is
  1. 12 ms1
  2. 18 ms1
  3. 27.11 ms1
  4. 22 ms1


Solution

The correct option is C 27.11 ms1
Given that, h=1 m,r=100 m,2x=1.5 m
For no skidding condition to satisfy, the component of normal reaction towards centre of circular curvature must provide the centripetal force & normal reaction's component in vertical direction must support the weight of carriage i.e mg
So, equation finally becomes:

mv2r=mgxh
v=grx1=9.8×100×0.751
v=27.11 ms1

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