An aeroplane is flying from city A to city B along path 1. The path 1 is a circular arc whose centre coincides with the centreof the earth. Another aeroplane is flying along path 2 from A to B. The path 2 is circular arc whose centre is at C. O is the centre of the earth. Then,

Options

A. The distance travelled by `1^(st)` aeroplane is greater than that of `2^(nd)`aeroplane.
B. The distance travelled by `1^(st)` aeroplane is less than that of `2^(nd)` aeroplane.
C. The displacement of both aeroplane is different.
D. None of these

Answer

(b)

Explanation

Let `I_1` = distance travelled by aeroplane 1 along path 1
`I_2` = distance travelled by aeroplane 2 along path 2
Let `OC = R/2`
Here, for path 1, `2 theta = l_1 /R`
But `costheta = R/2R = 1/2 therefore theta = pi/3`
`implies 2 xx pi/3 = l_1/R therefore l_1 = 2piR/3 = 0.67 piR`
But for path 2
`l_2 = pir = pi("AC") = pi Rsin pi/2 = sqrt 3/2 piR = 0.866 piR`
`therefore l_1 lt l_2`