Assume that the Earth is a spherical ball of radius x km with a smooth surface so that one can travel along any direction. If you have travelled from point P on the Earth’s surface along the East direction a distance of πx km, which direction do you have to travel to return to P so that the distance required to travel is minimum ?
East only
West only
East or West but not any other direction
Any fixed direction
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2023
The question states you travel “along the East direction a distance of πx km”. Travelling purely East means moving along a circle of latitude. A circle of latitude is a great circle only if it is the Equator (latitude 0).
If P is on the Equator, travelling East a distance πx along the Equator will take you to the point antipodal (exactly opposite) to P. Let this point be Q.
From Q (the antipodal point), the shortest distance back to P is along a great circle, and this distance is πx km. You can travel along the Equator back to P, either East or West. Both directions along the Equator lead to P in a distance of πx.
Other great circle paths from Q to P also exist, for instance, travelling North along a meridian to the North Pole (distance πx/2) and then South along a meridian from the North Pole to P (distance πx/2), totaling πx. Similarly, going via the South Pole takes πx. The initial directions from Q along these meridian paths are North and South respectively.
However, option C specifically limits the directions to “East or West but not any other direction”. This makes sense only in the simplified scenario where P is on the Equator, Q is antipodal, and the considered return paths are limited to East or West along the Equator. In this specific (likely intended) case, starting East or West from Q along the equator constitutes a minimum distance path back to P.