State whether the statement given below is true or false, giving reason in brief: "Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails"

Explanation

The weight of the body at rest on earth at equator considering spin motion of earth is given by
`W=m(g-Romega^(2))`
or `W=m[g-V^(2)/R] [as V=Romega]` ...(i)
Now if the train is moving in the direction of spin motion of earth i.e, from west to east with speed v relative to earth's surface, the velocity of train relative to the centre of earth will be `(V+v)` so
`W_(E)=m[g-((V+v)^(2))/R]` ....(ii)
Similarly for the train moving opposite to the motion of earth i.e, from east to west
`W_(W)=m[g-((V-v)^(2))/R]` ....(iii)
From Eqns. (ii) and (ii) and (iii) it is evident that `W_(E) lt W_(W)` So the pressure `(prop "weight")` will not be equal and the train going west will excert more pressure on the rails. SO the statement is false.