As shown in the figure, the cross-sectional area of the wider tube is 900 cm ^2 . If the boy standing on the piston weighs 45 kg , determine the difference in the water levels between the two tubes.

Step-by-step solution

Let the difference in water levels be h . The additional pressure exerted by the boy on the wider tube is balanced by the pressure due to the extra height of the water column in the narrower tube. Equating the pressures at the same horizontal level in both tubes: mg A = g h h = m A Given: Mass of the boy, m = 45 kg = 45000 g Cross-sectional area, A = 900 cm ^2 Density of water, = 1 g/cm ^3 Substituting the values: h = 45000 1 900 cm h = 50 cm