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Question

A train has to negotiate a curve of radius 2000 m. By how much should be the outer rail be raised with respect to the inner rail for a safe travelling speed of 72 kmh1?
The distance between the rails is 1 m.
(Take g=10 m/s2)

A
1 cm
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B
3 cm
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C
2 cm
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D
4.5 m
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Solution

The correct option is C 2 cm

Given,
v=72 km h1=72×518=20 m s1
Radius of curve, R=2000 m; l=1 m

Let h be the required height.

Applying Newton's 2nd law on train,

Ncosθ=mg

Nsinθ=mv2R

From both equation, we get after diving

tanθ=v2Rg .........(1)

Also from diagram,

tanθ=hl .......(2)

From eqs. (1) & (2),

hl=v2gR

h=v2lgR

After putting the values, we get

h=(20)2×110×2000=40020000

h=2100 m=2 cm

Hence, option (c) is correct.

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