Astudent sets a board to pivot about its center. the student then places a box with mass m at some position r from the pivot point. the student plans to place a second box with mass 2 m on the other side of the board. in terms of r, where should the box be placed in order to maintain static equilibrium?

The box should be placed at a distance of from the pivot

Explanation:

In order to be in static equilibrium, both Torques have to be the same magnitude, so:

  Replacing the formula for Torque:

  where X is the distance we need to find.

Solving for X we get:

As we can see, the distance does not depend on the actual value of the mass but on the fact of one being twice as much as the other one.