Question

A train of mass $m$ moves with a velocity $v$ on the equator from east to west. If $\omega$ is the angular speed of earth about its axis and $R$ is the radius of the earth then the normal reaction acting on the train is

• A. $mg[1-\frac{(\omega R-2v)\omega }{g}-\frac{v^2}{Rg}]$
• B. $mg[1-2\frac{(\omega R-2v)\omega }{g}-\frac{v^2}{Rg}]$
• C. $mg[1-\frac{(\omega R+2v)\omega }{g}-\frac{v^2}{Rg}]$
• D. $mg[1-2\frac{(\omega R+2v)\omega }{g}-\frac{v^2}{Rg}]$

Answer 1

Answer: (A)

$mg[1-\frac{(\omega R-2v)\omega }{g}-\frac{v^2}{Rg}]$

Earth rotates from west to east. Net velocity of train

$v_{net}=v-\omega R$

writing centrifugal force equation for train:

$mg-N=\frac{m{v}_{net}^2}{R}$

$N=mg-\frac{m(v-\omega R{)}^2}{R}$

$N=mg[1-\frac{(\omega R-2v)\omega }{g}-\frac{v^2}{Rg}]$