Pressure:
It is defined as force acting normally per unit area. Its SI unit is N/m2 or Pascal. Pressure is scalar quantity.
One Pascal Pressure:
The Pressure developed in 1m2 areas when force acting on it is 1 N is called 1 Pascal pressure.
Factors Affecting Pressure
i. Pressure at any point is directly proportional to the force applied. i.e. [PαF]
ii. Pressure is inversely proportional to the area in which force is being applied. [P α ]
Pressure Exerted by Liquid [p=hdg]:
Consider liquid of density ‘d’ is contained in a vessel of base area ‘A’ up to height ‘h’. Here, weight of liquid will exert pressure to the bottom of vessel.
= p = hdg
{\p=hdg}
Factors affecting liquid pressure:
i) Height or depth of liquid column.
ii) Density of liquid.
iii) Acceleration due to gravity.
Pascal’s Law:
If states that ‘Pressure exerted at any point in liquid enclosed in a closed container gets, transmitted equally in all direction.”
Application of Pascal’s Law,
Pressure at A=Pressure at B.
P1 = p2
=
As A1 > A2 then F1 > F2. So with small force can used to raise large object. So, hydraulic press is force multiplier.
Up thrust of a liquid:
The resultant upward force acted by a liquid when an object is immersed in it is called up thrust. Up thrust = wt of body in Air-wt. of body in liquid.
Density: It is defined as mass per unit volume.
D =
SI unit of density is kg/m3 and CGS unit is gm/cm3.
1000kg/m3=1gm/cm3
Relative Density: Ratio of mass of particular volume of substance to the mass of same volume of water at 40c is defined as relative density. It has no unit.
Up Thrust given by any liquid depends upon following factors:
i) Density of Liquid.
ii) Volume of liquid displaced by object.
iii) Acceleration due to gravity.
i.e. upthrust(U)=vdg
Up thrust given by a liquid doesn’t depends upon:
i) Depth of liquid.
ii) Weight of an object.
Any object immersed in liquid experiences two forces:
i) Weight of a body (acting downward)
ii) Up thrust (due to liquid upward)
Archimedes’ Principle:
It states, “When an object is wholly or partially immersed in a liquid, the weight of displaced liquid is equal to the upthrust of liquid on object.”
Upthrust = weight of displaced liquid.
Law of floatation:
“The weight of floating object is equal to the weight of liquid displaced”
Condition of floatation:
i) If density of substance is greater than density of liquid, it will sink.
ii) If density of substance is less than density of liquid it will float on liquid.
iii) If density of substance is equal to density of liquid, it will neither sink nor float but remains in equilibrium within the liquid.
Hydrometers
It is a device used to measure specific gravity (relative density) or density of liquid. It works based on principle of floatation. Hydrometers are of two types.
- Constant immersion hydrometer
- Constant weight hydrometer
Characteristics of Hydrometer:
i. Narrow long uniform stem, which increase sensitivity of hydrometer to give sharp reading on change.
ii. Big hollow bulb: It helps to make relative density of hydrometer to be less than of liquid.
- Small bulb with lead shot: It helps for vertical floating of hydrometer.
Important Formula for numerical
1. Pressure (P) =
2. Liquid pressure (P) = hdg
3. Hydraulic Machines =
4. Up thrust (U)= Adg (h2-h1), vdg; mxg
5. Up thrust (U) = wt of liquid displaced
= wt in air-wt in liquid
6. Law of floatation= wt of body = wt of liquid displaced
V1d1g = v2d2g
REASONABLE FACTS
1. The bottom of dam is wider and stronger
Ans- Liquid pressure is directly proportional to the depth of liquid from free surface. At the bottom of dam, there is high water pressure. To protect the dam from the high water pressure, the bottom is made wide and stronger than the upper part.
2. The pressure exerted by water at the bottom of the drum decreases slightly at the Himalayan region than that in the Terai region.
Ans: Since, pressure of a liquid is directly proportional to the value of g and the value of g is more at Terai region than that in the Himalayan region. So, the pressure exerted by water at the bottom of the drum decreases slightly at the Himalayan region than that in the Terai region.
3. The bucket filled faster in the downstairs tap than in upstairs tap.
Ans- Pressure of a liquid is directly proportional to its depth or height from the free surface. The tap at the downstairs is at greater height than the tap at the upstairs. Water comes out with greater pressure from the downstairs tap. So, bucket is filled faster in the downstairs tap than in upstairs tap.
4. The speed of flow of water out of a tap of upper floor is less than that of the down floor.
Ans- Since pressure of a liquid is directly proportional to its depth or height from the free surface. The height of the liquid column on the down floor is more than that on the upper floor. So the speed of flow of water out of a tap of upper floor is less than that of the down floor.
5. A deep sea-diver needs to wear diving suit.
Ans- The pressure of a liquid is directly proportional to the height of liquid column from free surface. When a person dives deep into sea, he or she has to bear high water pressure. To withstand with high water pressure, it is necessary to wear diving suit.
6. Weight of stone decreases in the salt solution.
Ans- When salt is dissolved in water, the upthrusts increases due to the increase in density of water (upthrust ¥ density of liquid). As a result, the weight of a stone decreases in the salt solution.
7. It is easier to lift a heavy stone inside the water.
Ans- The weight of the stone inside the water decreases due to the upthrust. So it is easier to lift a heavy stone inside the water.
8. The weight of a body is lighter in water than in air.
Ans- Upthrust due to water is greater than that of air. Upthrust decreases weight of body. Hence, the weight of a body is lighter in water than in air.
9. The weight of a body is more in vacuum than in air.
Ans- There is no upthrust in vacuum. Upthrust decreases the weight of body. Hence, the weight of body is less in air due to its upthrust.
10. It is easier to pull a bucket of water from the well until it is inside the water but difficult when it is out of water it is out of water.
Ans- Up thrust due to water is greater than that of air. Upthrust exerted by water decreases weight of body. Hence, It is easier to pull a bucket of water from the well until it is inside the water but difficult when it is out of water.
11. Studs are made on the sole of football player’s boot.
Ans- Studs are made on the sole of football player’s boot to increase the pressure on the ground that prevents the player from falling or sliding during sudden run and turning.
12. It is easier to cut vegetable with the sharp edged knife than the blunt one.
Ans- The area of the edge of sharp knife is less than that of the blunt one. So sharp edged knife can exert more pressure while applying force than that of the blunt edged knife as the pressure is inversely proportional to the area. Due to more pressure, it is easier to cut vegetables with the sharp edged knife than the blunt one.
13. Camel can walk easily on sand.
Ans- Camel has flat-soled feet which exert less pressure due to the body weight of camel. As there is less pressure exerted by flat-soled feet of camel, it can easily walk on the sand.
14. Buses and trucks have broad and double wheeled tyres.
Ans- The buses and trucks have to carry greater weight which exerts greater pressure on the tyres. The pressure on them is reduces by increasing the area of the tyres as the pressure is inversely proportional to the area.
15. The rear wheels of a tractor are made large and flat.
Ans- The rear wheels of a tractor are made large and flat to reduce the pressure and prevent the tyres from descending into the muddy land. As tractor is used for ploughing and threshing in crop fields, small and narrow real wheels may descend into the muddy and marshy land due to more pressure (i.e. P ¥ 1/A).
16. The wheel of tractor is wider than that of a car.
Ans- The tractor have to pass through muddy soil. Hence, the wheel of tractor is made wider to increase the area for reducing the pressure on a ground.
17. The water supply thanks are placed higher than any other building in a town.
Ans- The water supply tanks are placed higher than any other building in a town so that the pressure of water is more. Due to this, water can flow to the buildings located at higher level. As a result, water can be supplied easily on the taps of uppermost floors and houses built at higher level of the ground.
18. The gravity bulb of hydrometer is made heavier.
Ans- The gravity bulb of hydrometer is made heavier so that its centre of gravity remains very low, when it is floating in denser liquids. It helps the hydrometer to float upright in stable equilibrium.
19. Hydrometer has a heavy bulb and narrow stem.
Ans- Hydrometer has a heavy bulb to float in a liquid vertically. The stem of hydrometer is made long and narrow to find the relative density of less dense liquid i.e. it increases its sensitivity.
20. The floatation bulb (buoyancy bulb) of hydrometer is made small.
Ans- The floatation bulb of hydrometer is made small because denser liquids provide more upthrust and hence the whole hydrometer does not float on the dense liquid.
21. An egg sinks in fresh water but floats in a strong solution of salt (or in a saturated salt solution).
Ans- Fresh water has less density than that of the egg so the egg cannot displace water equal to its weight and it sinks. But salt on mixing with water increases the density of water and hence the egg can displace water equal to its weight and floats.]
22. Iceberg made up of water floats in water.
Ans- The density of ice is less than that of water. Due to this, iceberg is able to displace the water equal to its weight. Hence, Iceberg made up of water floats in water.
23. An iron nail sinks in water but a ship made up of iron floats.
Ans- Since the density of iron is greater than that of water, the iron nail sinks as the weight of the nail is greater than the weight of the displaced by it. But the ship made up of iron is designed in such a way that the relative density of ship becomes always less than that of water. Hence, the weight of water displaced becomes equal to the total weight of the ship and the ship floats.
24. It is easier for a man to swim in sea water than in river water.
Ans- The density of sea water is more than that of river water. Thus for the same volume, the sea water provides more upthrust as compared to the river water. So it is easier for a man to swim in sea water than in river water.
25. A hole at the bottom of a boat is more dangerous than that at the side.
Ans- The bottom of the boat exerts more pressure, as the force acts perpendicularly downwards, than that at the sides, If there is hole at the bottom of the boat, more water enters inside due to more upthrust and the boat may sink. So, a hole at the bottom of a boat is more dangerous than that at the side.
26. An iron nail sinks in water but floats in mercury.
Ans- The density of iron is more than that of the water. The iron nail cannot displace the water equal to its weight and it sink. But the density of mercury is much more than that of the water. It gives more upthrust which helps the iron nail to float on mercury.
27. A girl with heeled shoe exerts a higher pressure on the ground than an elephant.
And- The area of the heels of the girl’s shoes is much smaller in comparison with the area covered by the flat feet of the elephant (as P ¥1/A).As the pressure is inversely proportional to the Area, the pressure exerted by the heel is more. Hence, a girl with heeled shoe exerts a higher pressure on the ground than an elephant.
28. A man exerts more pressure under his foot when he stands with one foot than when he stands on two feet.
Ans- The area of one foot is less than that of two feet so a man exerts more pressure under his foot when he stands with one foot than when he stands on two feet as p ¥ 1/A.
29. The base of the house is made wider than its wall.
Ans- The walls and roof of house exerts pressure on the base of a house. The pressure exerted by the building is reduced by making the base of the house wider as pressure is inversely proportional to the area.
30. Hydraulic brakes are used.
Ans- The hydraulic brakes are used in heavy automobiles to stop them by applying a small force.
31. The loaded ship sinks more than empty ship.
Ans- The loaded ship has larger mass. Hence, the weight (or volume) of displaced water is more for loaded ship. But the empty ship has leser mass. Hence, the weight (or volume) of displaced water is less for empty ship. So the loaded ship sinks more than empty ship.
32. The hull of ship sinks more in fresh water than in sea water.
Ans- Upthrusts of liquid is directly proportional to density of liquid. The density of sea water is higher than that of fresh water of rivers. Hence, upthrust acting on a ship is higher in sea water than in the fresh water.
33. The food is cooked faster in pressure cooker.
Ans- The food is cooked faster in pressure cooker because the temperatures are high in pressure cooker. A pressure cooker does not allow for anything to escape at any significant amounts (unless the pressure inside gets too high and you hear the whistling sound.) with heat the gases inside wants to expend but because they are restricted to the volume of pressure cooker they cannot, so pressure builds up. At the pressure increase the food cooks quicker.
34. How does an aeroplane fly?
Ans- Planes fly by pushing or pulling air over a foil to produce lift. The pushing or pulling is called thrust and drag is the force of the air on the non foil parts of the plane. The foil creates lift with fast air (low pressure) giving over the wing and slower air (high pressure) under the wing. As soon as lift is greater than gravity the plane mores up.
[ foil= A device consisting of a flat or curved metal plate]
35. People staying at high attitudes have red cheeks.
Ans- At high altitude the level of oxygen is very less as compared to that of the lower region so, the process of respiration comes the red blood cell more active around the cheek. This causes to seem the red cheek of people living in high altitude.
36. The bottom of the ship is made heavier.
Ans- For the stable equilibrium center of gravity of a body or a system should lie as lower as possible. If the bottom of a ship is made heavy its center of gravity lies lower.
37. The gravity bulb of hydrometer is made hollow.
Ans-The gravity bulb of hydrometer is made hollow to make the relative density of hydrometer less then that of liquid so that it floats on it.
