Question

A hole is drilled through the center of Earth. The gravitational force exerted by Earth on an object of mass m as it goes through the hole is mg(r/R),where r is the distance of the object from Earth's center and R is the radius of Earth (6.4×106m).

A. Would this be a comfortable ride?

   

a)Going through the hole would be an uncomfortable ride because of the extreme temperature in the interior of Earth.

b)Going through the hole would be an uncomfortable ride since it takes too long to reach the spot on the opposite side of Earth compared with the flight by airplane halfway around Earth to this spot at 300 m/s.

c)This would be a comfortable ride.   

B. How does one-half this time compare with the time needed to fly in an airplane halfway around Earth? Assume that the speed of the airplane is 300 m/s.

Answer 1

(A) Gravitational force exerted by the earth on the object, F = mg(r/R)

So, when the value of 'r' is small, the value of F will also be small.

And at the center of the earth, where r = 0

F will also be equal to 0.

Now, when the value of F is 0, the object will come to stand still condition and the object will have no velocity.

So, infinite time will be taken by the object to cross the center of the earth.

Hence, option (b) is the correct answer.

(B) If we are travelling by airplane, then to reach at the other side of the earth, we have to cover a distance of d = 2*R = 2x6.4 x 10^6 m = 1.28 x 10^7 m

Speed of the airplane = 300 m/s

Therefore, time taken by the airplane, t = (1.28 x 10^7) / 300 = 42667 s = 11.85 Hours.

Note that in the first case, time taken by the object is infinity.

So, one-half of this time is also equal to infinity.