# Find the time required to to cover the length of the tunnel.

1. Mar 7, 2005

### npgreat

A tunnel is dug through the centre of the earth.A particle is projected into it with a velocity =(gR)^1/2.Find the time required to to cover the length of the tunnel.
The force of attraction is F=GMmx/R^3 where x=distance from centre
Then the time period is T=2*3.14*(R^3/GM)^1/2
And the answer comes out to be Half of the time period
But I am not understanding what to do with the initial velocity.

Last edited: Mar 8, 2005
2. Mar 7, 2005

### stunner5000pt

Perhaps you should us some of your attempted work? then maybe someone would approach. But since im nice and all

yes it is simple harmonic motion so then in general SHM equation is
$$m \frac{d^2 r}{dt^2} + b \frac{dr}{dt} + kr = F$$

since this is tunnel taht doesnt depend on its sides no b and certainly no F value. All you're left with a k value.

sooo you're left with what?? What is the k????
Here that radial distance is not constant! Instead The k value is dependant on the distnace form thcentre of the earth. See how you could fit your gravitational force formula into the k value. after you have k you can figure out the period, can't you??