1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Ball dropped through a tunnel through the earth.

  1. Aug 30, 2014 #1
    1. The problem statement, all variables and given/known data

    A tunnel is drilled from the surface of the earth(mass assumed to be M and radius to be R) to its center . A body of mass m is dropped from the surface to the center through the tunnel. What will be the velocity with which the body of mass m will hit the tunnel.

    2. Relevant equations

    Loss in PE = Gain In KE

    Loss in PE = PE at surface - PE at center of earth.

    = |-GMm/R - 0|

    1/2 mv[2] = |-GMm/R|

    v = √(2GM/R)

    3. The attempt at a solution

    But in a textbook , the PE at the center of earth is given to be -(3/2) (GMm/R)

    what is the right way of approaching the problem.
  2. jcsd
  3. Aug 30, 2014 #2


    User Avatar
    Gold Member

    The point where the potential energy is zero, is arbitrary. You assumed it to be the centre of the earth which is not in agreement with problem's assumption. Of course you can solve the problem with your current assumption too.
  4. Aug 30, 2014 #3

    I like Serena

    User Avatar
    Homework Helper

    Let's assume that ##R## is the radius of the planet, and ##r## is the distance between the body and the center.

    Then the attractive force is not just ##F=-\frac{GMm}{r^2}##.
    The value of ##M## that you should use varies with ##r##, since we're inside the planet.

    The ##M## that contributes is the mass in the sub sphere that is still between you and the center of the planet. To calculate it, we need to assume for instance that the mass density is constant.

    What would the mass ##M(r)## of the sub sphere of radius ##r## be?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted