Question

a. Suppose the earth were wrapped tightly in a 25,000 mile belt. Now suppose someone adds 1 mile to the belt. If the belt is raised uniformly above the earth’s surface, how high above the surface will it be? Give your answer in feet. (Guess first, before you calculate this.)

b. This time, suppose someone adds 1 foot to the belt. Again, raise the belt uniformly above the earth’s surface—how high will the belt be? Give you answer in inches.

c. Finally, suppose a regulation NBA basketball is wrapped tightly in a 29.5 inch belt. Now suppose someone adds 1 foot to the belt. If the belt is raised uniformly above the ball’s surface, how high will it be? Give your answer in inches. Are you surprised by this result?

Answer 1

Ans:

a) Length of the belt = 25000 mile

which is also equal to the circumference of the earth

Therefore we can find out the radius of the circle as shown below

Now when 1 mile is added to the belt the new circumference of the belt will be = 25001 mile

Therefore the new radius of the belt will be given by

Therefore the difference between the two radii is the height by which the belt will rise above the surface

b) In this case 1 foot is added to the belt

Now 1 foot = 0.000189394 miles

There the new radius will be

Therefore the height of the belt above surface is

c) Now here total length of the belt = 29.5 inch

Therefore the radius of the ball is

Now 1 foot is added to the belt

1 foot = 12 inch

Therefore new length of the belt = 29.5+12=41.5

Therefore new radius of the ball is

Therefore the height of the belt from surface is

As the diameter of the ball is very small compared to the diameter of the earth the little increase in the length of the belt results in more increase in height of the belt above the surface as compared to the case of earth.