Physics
A simple U tube contains mercury to the same level in both of it's arms. If water is poured to a height of 13.6 cm in one arm, how much will be the rise in mercury level in the other arm ?
Given: density of mercury = 13.6 x 103 kg m-3 and density of water = 103 kg m-3
Answer
Given,
ρm = 13.6 x 103 kg m -3
ρw = 103 kg m -3
Height to which water is poured in one arm, hw = 13.6 cm
By pouring 13.6 cm of water, the mercury level in the left arm goes down to point A by x cm, while in the right arm, it rises to point C by x cm. Therefore, BC = hm = 2x cm
By Pascal's law,
Pressure in the water column = pressure in the mercury column
Therefore, PA = PB
⇒ hw ρw g = hm ρm g
⇒ 13.6 x 103 x g = 2𝑥 x 13.6 x 103 x g
⇒ 1 = 2𝑥
⇒ 𝑥 = 1/2 = 0.5 cm
Hence, the rise in mercury level = 0.5 cm
Related Questions
What should be the ratio of area of cross section of the master cylinder and wheel cylinder of a hydraulic brake so that a force of 15 N can be obtained at each of it's brake shoe by exerting a force of 0.5 N on the pedal ?
(a) Calculate the height of a water column which will exert on it's base the same pressure as the 70 cm column of mercury. Density of mercury is 13.6 g cm-3.
(b) Will the height of the water column in part (a) change if the cross section of the water column is made wider ?
The pressure of water on the ground floor is 40,000 Pa and on the first floor is 10,000 Pa. Find the height of the first floor.
(Take : density of water = 1000 kg m-3, g = 10 m s-2)In a hydraulic machine, a force of 2 N is applied on the piston of area of cross section 10 cm 2. What force is obtained on it's piston of area of cross section 100 cm 2?