Question

A U-tube is filled with water, and the two arms are capped.(Figure 1) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube.

A) If a 1.0-kg-mass block is on the left cap, how much total mass must be placed on the right cap so that the caps equilibrate at equal height?

Answer 1

Let A1 is the ara of the left cap and A2 is the area of right cap.

Let m1 = 1 kg

m2 = ?

A1 = pi*r^2

A2 = pi*(2*r)^2

= 4*pi*r^2

= 4*A1

Apply, Pascal's law,

When the liquid is at the same height

P1 = P2

F1/A1 = F2/A1

m1*g/A1 = m2*g/A2

m1/A1 = m2/A2

==> m2 = m1*(A2/A1)

= 1*(4*A1)/A1

= 4 kg <<<<<<<-----------Answer