Physics Notes: Mass, Weight and Density - 2018

MASS

The mass of a body is the quantity of matter contained in it. It is a scalar quantity.

SI unit = kg
Note: Mass of a body does not change from place to place and remains constant.

WEIGHT

The weight of a body is the force with which it is attracted towards the centre of the earth.
Weight of a body (w) = mg
Note: Weight of a body is not constant, it changes from place to place.

Important Facts about weight:-
☛ Weight of a Body in a Lift
When lift is rest or in uniform motion the weight recorded in spring balance (i.e. apparent weight) is equal to the real weight of the body w = mg.

☛ When lift is accelerating upward the weight recorded in spring balance is greater than then real weight of the body
w‘ = m(g + a)

☛ When lift is accelerating downward the weight recorded in spring balance is smaller than the real weight of the body
w‘ = m(g – a).

☛ When lift is falling freely under gravity the apparent weight of the body
w' = m (g – g) (∵ a = g)
w‘ = 0
Therefore, body will experiences weightlessness.

☛ Weight of a Body at the Moon
As mass and radius of moon is lesser than the earth, so the force of gravity at the moon is also less than that of the earth. It‘s value at the moon‘s surface is g/6.

DENSITY

The density of water is 1000 kg/M³

The density of water is maximum at 4°C
Hydrometer It is an instrument used to measure density or relative density of liquid. Its working is based on law of floatation.

Important facts about density:
☛ It is easier to swim in sea water than in a river as density of sea water is greater than the density of river water. In sea water, buoyant force is greater than that in river water.

☛ The density of human body is less than the density of water but the density of human head is greater than the density of water. Therefore, during swimming a person displaces the liquid with hands and legs and total weight of displaced liquid becomes equal to the weight of the body.

SPEED

The distance covered by a moving body in a unit time interval is called its speed.

Speed = Distance Travelled/ Time Taken

VELOCITY

The time rate of change of displacement of a body is called its velocity
Velocity= Displacement/ Time

An object is said to be moving with uniform velocity if it undergoes equal displacements in equal intervals of time.
An object is said to be moving with non-uniform or variable velocity if it undergoes unequal displacement in equal intervals of time.

ACCELERATION

The time rate of change of velocity of a body is called its acceleration.

Acceleration = Change in velocity/ Time taken
It is a vector quantity and its SI unit is m/s-2
Acceleration at an instant of time is known as instantaneous acceleration.
When the velocity of a body increases with time, then its acceleration is positive and if velocity decreases with time, then its acceleration is negative called deceleration or retardation.
If acceleration does not change with time, it is said to be constant acceleration.

Q1.Mass of oil is 11040 kg and volume is 12 m³, its density would be?
Sol.
Density = Mass/Volume
= 45 g / 15 cm³ = 3.0 g/cm³

Q2.You decide you want to carry a boulder home from the beach. It is 30 centimetres on each side, and so has a volume of 27,000 cm3. It is made of granite, which has a typical density of 2.8 g/cm3. How much will this boulder weigh?
Sol.
Mass = Volume × Density
= 27000 cm³ × 2.8 g/cm³
=75600 grams

Q3.A 75 kg man stands on a scale in an elevator. When the elevator begins to rise, the scale reads 100 kg. What was the acceleration in factors of g?
Sol.
The Scale is reading the Normal Force
mg+ma= 100 kg
m(g+a)=100 kg.....I
mg = 75 kg......II
Dividing I & II
4/3= (g+a)/g
4/3 = 1 + a/g
1/3 = a/g
a = (1/3)g