Advertisements
Advertisements
Question
A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit?
Advertisements
Solution 1
The given system of water, mercury, and methylated spirit is shown as follows:
Height of the spirit column, h1 = 12.5 cm = 0.125 m
Height of the water column, h2 = 10 cm = 0.1 m
P0 = Atmospheric pressure
ρ1 = Density of spirit
ρ2 = Density of water
Pressure at point B = `P_0 + h_1rho_1g`
Pressure at point D = `P_0 + h_2rho_2g`
Pressure at points B and D is the same.
`P_0 + h_1rho_1g =h_2rho_2g`
`rho_1/rho_2 = h_2/h_1`
= 10/12.5 = 0.8
Therefore, the specific gravity of spirit is 0.8.
Solution 2
For water column in one arm of U tube, h1 = 10.0 cm; ρ1 (density) = 1 g cm-3
For spirit column in other arm of U tube, h2 = 12.5 cm; ρ2 =?
As the mercury columns in the two arms of U tube are in level, therefore pressure exerted by each is equal.
Hence h1ρ1g = h2ρ2g or ρ2 = h1ρ1/h2 =10 x 1/12.5 = 0.8 g cm-3
Therefore, relative density of spirit = ρ2/ρ1 = 0.8/1 = 0.8
APPEARS IN
RELATED QUESTIONS
Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain.
A satellite revolves round the earth. Air pressure inside the satellite is maintained at 76 cm of mercury. What will be the height of mercury column in a barometer tube 1 m long placed in the satellite?
The three vessels shown in the following figure have same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be
A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will be ______.
Figure shows a capillary tube of radius r dipped into water. If the atmospheric pressure is P0, the pressure at point A is
The heights of mercury surfaces in the two arms of the manometer shown in figure are 2 cm and 8 cm.
Atmospheric pressure = 1.01 × 105 N−2. Find (a) the pressure of the gas in the cylinder and (b) the pressure of mercury at the bottom of the U tube.
The weight of an empty balloon on a spring balance is W1. The weight becomes W2when the balloon is filled with air. Let the weight of the air itself be w. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon.
(a) W2 = W1
(b) W2 = W1 + w
(c) W2 < W1 + w
(d) W2 > W1
A glass full of water has a bottom of area 20 cm2, top of area 20 cm2, height 20 cm and volume half a litre.
(a) Find the force exerted by the water on the bottom.
(b) Considering the equilibrium of the water, find the resultant force exerted by the sides of the glass on the water. Atmospheric pressure = 1.0 × 105 N/m2. Density of water 1000 kg/m3 and g = 10 m/s2. Take all numbers
to be exact.
Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out. (a) What will be the answers to the problem? (b) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.
If water be used to construct a barometer, what would be the height of water column at standard atmospheric pressure (76 cm of mercury) ?
Water is filled in a rectangular tank of size 3 m × 2 m × 1 m. (a) Find the total force exerted by the water on the bottom surface on the tank. (b) Consider a vertical side of area 2 m × 1 m. Take a horizontal strip of width δx metre in this side, situated at a depth of x metre from the surface of water. Find the force by the water on this strip. (c) Find the torque of the force calculate in part (b) about the bottom edge of this side.
(d) Find the total force by the water on this side.
(e) Find the total torque by the water on the side about the bottom edge. Neglect the atmospheric pressure and take g = 10 ms−2.
A U-tube containing a liquid is accelerated horizontally with a constant acceleration a0. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.
Water leaks out from an open tank through a hole of area 2 mm2 in the bottom. Suppose water is filled up to a height of 80 cm and the area of cross section of the tanks is 0.4 m2. The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank. (a) Find the initial speed of water coming out of the hole. (b) Find the speed of water coming out when half of water has leaked out. (c) Find the volume of eater leaked out using a time interval dt after the height remained is h. Thus find the decrease in height dh in terms of h and dt.
(d) From the result of park (c) find the time required for half of the water to leak out.
Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh?
Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is p0.
