Question

Dave Kunst is the first person verified to have completely circled the entire earth on foot in 4 years. Let us assume he traveled in a perfect circle around the earth and the center of his circle is same as the center of the earth. If he traveled through a tunnel through the center of the earth penetrating to other side of earth at the same average speed, how much time would he have taken?

• A. 4.55 years
• B. 2 years
• C. 3.55 years
• D. 1.27 years

Answer 1

The correct option is D 1.27 years

Let 'D' be the diameter of the Earth.
Then, distance covered will be the perimeter of the circle,
$d=\pi D$
Time taken, $t=4years$

From defintion of speed,
$v=\frac{d}{t}$
$v=\frac{\pi D}{t}......\left(i\right)$

If he travelled across the tunnel, he would cover a distance equal to the diameter of the earth. So, new distance is:
$d^{\prime }=D$
Let new time taken be $t^{\prime }$.
It is given that the speed of the man in both the cases is same. Hence, again using defintion of speed,
$v=\frac{d^{\prime }}{t^{\prime }}$
$v=\frac{D}{t^{\prime }}......\left(ii\right)$

Equating (i) and (ii), we get:
$\frac{\pi D}{t}=\frac{D}{t^{\prime }}$
$t^{\prime }=\frac{t}{\pi }$
$t^{\prime }=\frac{4}{\pi }$
$t^{\prime }=1.27years$