Question

46. A train 1 moves from east to west (clockwise) and another train 2 moves from west to east (anticlockwise)
on the equator with equal speeds relative to ground. The ratio of their centripetal accelerations a1/a2 relative to centre of earth is:
(1) > 1
(2) = 1
(3) < 1
(4) >=1​

Answer 1

Answer:

e earth rotates from west to east.

If we view from the center of the earth, the trains will be performing Circular Motion.

So, speed of the train that moves from west to east will be greater than that of the train moving from east to west;

as, Speed of train moving from west to east=Speed of the train+wR

and,

Speed of train moving from east to west=Speed of the train−wR 

where

w=angular speed of rotation of the earth

R=radius of the track

And 

Centrifugal force =

where, m is the mass of the object in circular motion, v is its speed and R is the radius of the circular track.

and by force balance we get



mg is the force due to gravity, N is the normal reaction from the track.

Assuming mg is same

 train with greater centrifugal force will exert less normal force on the track and the train with greater speed will exert greater centrifugal force. Thus, the train moving from west to east will exert less force and the train moving from east to west will exert greater force on the track.

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