(C) The banking of rails is given by the formula $\tan \theta = \frac{h}{d} = \frac{v^2}{rg}$,where $h$ is the elevation,$d$ is the distance between r

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(C) The banking of rails is given by the formula $\tan \theta = \frac{h}{d} = \frac{v^2}{rg}$,where $h$ is the elevation,$d$ is the distance between rails,$v$ is the velocity,$r$ is the radius of curvature,and $g$ is the acceleration due to gravity.Given: $v = 20 \, m/s$,$r = 40,000 \, m$,$d = 1.5 \, m$,and $g = 10 \, m/s^2$.Substituting the values: $\frac{h}{1.5} = \frac{(20)^2}{40,000 \times 10}$.$\frac{h}{1.5} = \frac{400}{400,000} = \frac{1}{1000}$.$h = \frac{1.5}{1000} \, m = 0.0015 \, m$.Converting to $mm$: $h = 0.0015 \times 1000 \, mm = 1.5 \, mm$.

Class 11 Physics 3-2.Motion in Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

A
$2.0$
B
$1.75$
C
$1.50$
D
$1.25$

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3-2.Motion in Plane

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

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