☆ physical quantity-
• A quantity that can be measured is called a physical quantity.
Or a measurable quantity is called a physical quantity.
• a physical quantity can be of two types:
1. Scalar quantity- which can be expressed only by their magnitude.eg. mass, length, time ,distance, density ,volume, speed, temperature, work, energy, power, pressure etc.
2. Vector quantity- which requires the magnitude as well as the direction to express them.eg. force ,weight, velocity , displacement ,acceleration,magnetic field ,moment of force etc.
• physical quantity= magnitude× unit
• basic quantities or fundamental quantities with their S.I. units:
1. Length - metre- m
2.Mass- kilogram- kg
3. Time- second-s
4. Temperature- Kelvin-K
5. Luminous intensity- candela-cd
6. Electric current- ampere-A
7. Amount of substance-mole-mol
☆ measurement-
- measurement is a comparison of an unknown quantity with a known fixed quantity of the same kind.
*Density:
- equal masses of different substances have different volumes.
•equal volumes of different substances have different masses.
*Mass per unit volume of a substance is called as its density.
-word formula:
Density=mass / volume.
ρ= M/ V
ρ=density
M=mass
V=volume
-S.I. unit of density is kg/m³
-CGS unit of density is g/cm³
•relationship between SI & CGS unit of density
1kg/m³= 1kg / 1m×1m×1m
=1000g / 100cm×100cm×100cm
= 1g /1000cm³
=1g /10³ cm³
= 10-³ gcm-³
1kg/m³ = 10-³ gcm-³
1gcm-³ = 1000 kgm-³
-Density of iron=7.8 gcm-³
-density of copper=8.9 gcm-³
-density of water=1 gcm-³
•density of a substance does not change with any change in its shape or size.
•density decreases with increase in temperature and density increases with decrease in temperature for all substances except few.
*Maximum Density of water is 1gcm-³ at 4 degree Celsius.
water contracts on heating from 0 degree Celsius to 4 degree Celsius and expands on heating above 4 degrees celsius.so the density of water increases from 0 degree Celsius to 4 degree Celsius and then decreases above 4 degree Celsius.
*Determination of density of a regular solid:
1. Measuring mass by putting the substance on a beam balance.
2. Finding volume by either formula method or liquid displacement method.
3. Putting the values of mass and volume in the formula
Density=mass/volume.
Formula for finding the volume of some regular solids:
1. Volume of a cube=side×side×side
2. Volume of a cuboid=length×breadth×height
3. Volume of a sphere=4/3 πr³
4. Volume of a cylinder=πr²h
5. Volume of a cone=1/3 πr²h
6. Volume of a lamina whose area is A and thickness is h, = A×h
Vessels for measuring volume:
1. Measuring cylinder -it is graduated in millilitre (mL).
-the graduation increase upwards.
-it comes in different capacities such as 100mL,200mL,500mL etc.,
•area of cross section of 10 centimetre square is is made up of either glass or plastic.
• it is is of capacity 100cm³ or 100mL.
• used in laboratory to measure the volume of liquids.
• used to find the volume of an irregular object by measuring the displacement of water or liquid by the object.
2. Measuring beaker-
-it is used to to take out fixed volume of liquids.
-the capacity of a measuring beaker is Marked on it.eg. 50mL,100mL,200mL,500mL,1L etc.,
3.Eureka can-
-the Beaker can contain a volume of liquid up to the spout.
-any excess of liquid over flows through the spout.
*Determination of density of an irregular solid:
1. Mass of a body is calculated by keeping it on on the beam balance.
2. Volume is calculated by liquid displacement method.
Liquid displacement method-
•volume of irregular shaped body is measured by using a measuring cylinder by the method of displacement of liquid.
• volume of a body of irregular shape= volume of liquid displaced by the body when it is immersed completely into the liquid.
• the difference in the final level from the initial level gives the volume of the liquid displacedi.e., V=V₂ -V₁. V₂=final level ,V₁=initial level.
*Density bottle:
-a density bottle is a specially designed to determine the density of a liquid.
-sometimes it is also called as specific gravity bottle.
-it stores a fixed volume of a liquid.
-the stopper has a narrow hole through which the excess liquid drains out.
-it contains the same volume of liquid when it is filled.
-the volume of bottle is either 25 ml or 50 ml.
*Determination of density of a liquid using a density bottle:
1. Mass of empty bottle M₁
2. Mass of bottle filled with water M₂
3. Mass of bottle filled with liquid M₃
These masses are measured by using beam balance.
4. The mass of liquid M = M₃ - M₁
5. Volume of liquid. V=M₂ - M₁
6. By using formula of density as,
Density=mass of liquid/volume of liquid.
ρ=M/V
ρ=(M₃ - M₁) / M₂ - M₁
Here M2 - M1= V we will get in centimetre cube.
Density of water=mass/volume
Density×volume=mass
Volume=mass/density. But density of water=1g/cm³
Units of mass and density's gram,gets cancelled and cm³ is left as a unit.
*Relative Density:
-the ratio of density of the substance to density of water is called relative density.or
-relative density is the ratio of the mass of any volume of the substance to the mass of an equal volume of water at 4°C.
-represented as R.D
-word formula:
R.D=density of the substance/density of water at 4 degree Celsius.
-R.D is a dimensionless quantity because it is the ratio of two same quantities.
-*measurement of relative density of a liquid:
-the relative density of a liquid is measured by using a density bottle.
1. Mass of empty bottle= M₁ g
2. Mass of bottle filled with water =M₂ g
3. Mass of bottle filled with liquid= M₃ g
4. Mass of water=(M₂ - M₁)g
5. Mass of liquid=(M₃ - M₁)g
These masses are measured by using a beam balance.
Relative density of a liquid=mass of liquid/mass of equal volume of water.
R.D= (M₃ - M₁)g/(M₂ - M₁)g
=(M₃ - M₁)/(M₂ - M₁)
*Specific gravity means relative density with respect to water.
*Density of substance in its different states:
--the substance is highly dense in solid state, less dense in liquid state and still less dense in gaseous state.
-but the density of ice is 0.917g cm-³,water is 1.00gcm-³ & steam is 0.00057 gcm-³.
-a body floats on a liquid if its density is less than the density of the liquid, while a body sinks in a liquid if its density is more than the density of the liquid.
-principle of floatation-
-when a body is placed in a liquid then two forces act on it:
1. The weight of the body which axe in vertically downward direction and has a tendency to sink the body.
2. Buoyant force/upthrust acts vertically upwards and it has tendency to move the body up.
Case 1-the weight of body is greater than the buoyant force-the body will sink in the liquid to the bottom under the the influence of the resultant force.
Case 2- the weight of the body is equal to the buoyant force.-the body will float just inside the surface of liquid.
case 3-the weight of the body is less than the buoyant force. Body floats partially submerged in liquid.only that much portion of the body will immerse inside the liquid by which the weight of the liquid displaced balance is the total weight of the body.
*Law of floatation:
- weight of the floating body= weight of the liquid displaced by its immersed part.
-the apparent weight of a floating body is zero.
*Body while floating,sinks deeper in a liquid of low density than in a liquid of high density.
*Some applications of floatation:
1. Floatation of an iron ship-average density of ship is less than the density of water.
2 flotation of man-the weight of a man gets balanced by the less immersed part of his body in sea water as compared to that in river water. Density of seawater is more than the river water because of presence of salt.
3. Floatation of ice on water- 9/10 th part of ice is inside the water & only 1/10 th part of it outside water. Because the density of ice is 0.9gcm-³ & water is 1.0gcm-³.
4. Submarine- submarine is provided with water tanks to vary its average density.
5.icebergs-very huge and large pieces of ice floating on sea water.it floats in water with its large person submerged inside the water and only a little portion of it is above the surface of water.
6.whales-whales have a special organ called swim bladder to vary its average density.
7.Balloons-the buoyant force experienced by the balloon due to air, becomes greater than the weight of the balloon. So, the balloon rises up under the influence of the net upward force.
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