A uniform capillary tube closed at one end, contained air trapped by a thread of mercury 85 mm long. When the tube was held horizontal, the length of the air column was 50 mm. When it was held vertically with the closed end downwards, the length was 45 mm. Find the atmospheric pressure in Pa. (Density of mercury = 14 x 103 kg/m3 )
The pressure of a gas is measured using a manometer as shown in the diagram.
The mercury in the manometer is replaced with a liquid which is less dense. How does the value of h change?
A It becomes zero.
B It decreases, but not to zero.
C It stays the same.
D It increases.
Solutions: Option D
The pressure to be measured remains constant. Since P = pgh, where p is the density of the liquid used in the manometer. If a liquid of lower density is used, height h of the liquid (level difference) will be greater. The gravitational field strength g remains constant.
(a) (i) A bigger force than F can be obtained due to the level system and hydraulic system.
Level system: Applying principle of moments, the anticlockwise moment by the F is equal to the clockwise moment by the force on piston A (note that the handle is pushing the piston down, but the piston A is pushing on the handle upwards – action = reaction). As the perpendicular distance from F to the pivot is greater than the perpendicular distance of the force by piston to the pivot, the force on the piston A is greater than F at handle.
Hydraulic system: As the pressure transmitted in the liquid is the same, pressure at piston A = pressure at piston B. As P = F/A and area of piston A is smaller than area of piston B, a larger force is obtained in piston B.
Hence these two systems allow the force on piston B to be greater than F at the handle.
(a) (ii) Both liquid and gas molecules are in a continuously random motion. But in liquid, the molecules are closely packed together and able to slide around one another. There is very little empty space between the molecules hence liquid is not compressible. Gas molecules are far apart from one another, hence gas can be easily compressed.
(b) P = F/A = 12000 / 0.060 = 200 000 Pa
(c) Velocity is the vector quantity while speed is a scalar. As the car goes round the bend, the direction of the car changes. Hence velocity is changing even though speed is constant.
Likewise, as the velocity is changing, the car is considered to have an acceleration (not in the sense of increasing speed though).