Question

A tunnel is dug from the surface of the earth through the center and opens at the other end. a ball is droppedfrom one end of the tunnel. the acceleration due to gravity on the earth's surface is g and the radius of the earthis r. assuming that the earth has a constant density, the time taken by the ball to reach the center of the earth is

Answer 1

Answer:

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Answer 2

Time taken by a body to reach at the center is ½t ie 42.3 minutes.

If we dug the earth through the center and make a body to fall through that, then that body will follow a Simple harmonic motion (SHM) throught out the time.

.) We know that in Simpe Hharmonic Motion time period is given by t = 2π √ (L/g)

Where L is the length and g is the acceleration due to gravity.

.) Now in the case of Earth ,

t = 2π √(r /g) --------(1)

Where r is the radius of the Earth

Now ,

We known r = 6.4*10^6 m and value of g = 9.8 m/sec^2

.) Now putting the values in equation (1) we get ,

t = 84.6 min => ½t = 42.3 minutes