2 boys weighing 40 kg and 50 kg are sitting on either sides of a wooden plank at distances 4 - Physics - System Of Particles And Rotational Motion

Question

2 boys weighing 40 kg and 50 kg are sitting on either sides of a
wooden plank at distances 4 5m and 1 5m respectively feom the
fulcrum coinciding with the centre of gravity of the plank Where
must a third boy of weight 35kg sit to secure balance?

Sanjay Singh · Accepted Answer

Dear student
Let 40 kg boy sits on the left of the fulcrum than torque of its weight about the fulcrum in anticlockwise direction isT1 =40×10×4
5=1800NmLet 50 kg boy sits on the right of the fulcrum than torque of its weight about the fulcrum in clockwise direction isT2=50×10×1
5=750NmAnticlockwise torque is greater than the clockwise torque so the other boy must sit to provide clockwise torque so it should sit right of fulcrum
Let the boy sits at a distance xfrom thefulcrumthan the torque of its weight about thefulcrum is T3=35×10×xFor equibrium clockwise torque=anticlockwise torque50×10×1
5+35×10×x=40×10×4 550×1
5+35×x=40×4
575+35x=18035x=180-7535x=105x=10535=3mRegards

2 boys weighing 40 kg and 50 kg are sitting on either sides of a wooden plank at distances 4.5m and 1.5m respectively feom the fulcrum coinciding with the centre of gravity of the plank. Where must a third boy of weight 35kg sit to secure balance?