Question

A boy and a girl have masses of 45 kg and 32 kg respectively. Both are balanced on the opposite ends of a 5.0 m long wooden plank with a mass of 16 kg. At what point along the plank does the pivot point have to be?

Answer 1

here the plank is in equilibrium only if the torques on both sides are equal .but the problem is with the mass of the plank . let the plank be having a mass per unit length "p"
then p=16/5.
now we can find torques on each side of the pivot
on the left side torque = 45*x + x/2 * (x*p) {****** this is the torque by the planks weight , the plank to the left has a wight of p*x and this weight acts at midway x/2}
similarly on the right side torque =32*(5-x) + (5-x)/2 * (p* 5-x)
now solve for x