IB HL Physics Tetrahedron Problems

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A sheet of questions where the geometry of the problem involves a regular tetrahedron.

  1. Six resistors R are placed as the sides of a regular tetrahedron. Show that the total resistance across two corners of the tetrahedron is R/2.
  2. Four point charges are placed at the vertices of a regular tetrahedron. Show that the magnitude of the resultant force acting on one of the charges is √6 x the force between two of the charges.
  3. A solid uniform tetrahedron of mass M and side L is rotated about an axis through a vertex that is perpendicular to the opposite side. Show that the moment of inertia of the tetrahedron about this axis is M L2/20.
  4. Four masses M are placed at the vertices of a regular tetrahedron of side L and released from rest. Show that the time taken for the masses to meet is π √( L3/(32G M) ).
  5. A triangular pyramid is a regular tetrahedron of mass M and side L. Find the work done in lifting the material from ground level to build the triangular pyramid.
  6. A regular tetrahedron of side L and density 𝜌1 floats vertically with its base downwards in a fluid of density 𝜌2, 𝜌1< 𝜌2. Find the period of small vertical oscillations of the tetrahedron when 𝜌1/ 𝜌2 = 2/5 , g = 9.8 m s-2 and L = 100 m.