Physical Science Classes VI-X for School Assistants and TET Paper 2A · Chapter 2

Laws of Motion, Force, Friction, Pressure, Gravitation and Buoyancy

What to remember

Newton's laws: (1) a body keeps its state of rest or uniform motion unless a net force acts (inertia); (2) F = ma, or force = rate of change of momentum; (3) action and reaction are equal and opposite and act on different bodies.
Gravitation: F = G m₁m₂/r², with G = 6.67 × 10⁻¹¹ N m²/kg²; g = 9.8 m/s² near Earth; mass is constant but weight depends on g.
Pressure = force ÷ area (pascal); buoyant force equals the weight of the liquid displaced (Archimedes); a body floats if its density is less than that of the liquid.

Force and the first law

A force is a push or pull that can change the state of rest or motion, speed, direction or shape of a body. Unit: newton (N). Force is a vector. Balanced forces (net force zero) do not change the state of motion; unbalanced forces produce acceleration.

Newton's first law (law of inertia): every body continues in its state of rest or of uniform motion in a straight line unless an external unbalanced force acts. Inertia is the tendency of a body to resist change in its state. Mass is the measure of inertia: a heavier body has more inertia.

Examples: a passenger jerks forward when a bus brakes suddenly (inertia of motion); dust falls when a carpet is beaten (inertia of rest); a coin drops into the glass when the card under it is flicked away.

Momentum and the second law

Linear momentum p = mv (vector). Unit kg m/s.
Second law: the rate of change of momentum is proportional to the applied force and takes place in the direction of the force. For constant mass: F = ma. 1 newton is the force that gives a mass of 1 kg an acceleration of 1 m/s².
Impulse = force × time = change in momentum (F·t = mv − mu). Unit N s (same as kg m/s). Cricketers draw their hands back while catching a ball to increase the time and reduce the force; vehicles have airbags and cushions for the same reason.
Example: F on a 5 kg body gives a = 2 m/s²: F = 10 N. A 2 kg ball changing speed from 3 m/s to 8 m/s in 0.5 s: F = 2 × 5 ÷ 0.5 = 20 N.

Third law and conservation of momentum

Third law: to every action there is an equal and opposite reaction. Action and reaction act on different bodies, so they do not cancel each other. Examples: recoil of a gun, rocket propulsion, walking (we push the ground back, the ground pushes us forward), swimming, a boat moving backward when a person jumps out.

Law of conservation of momentum: if no external force acts, the total momentum of a system remains constant. Example: a bullet of mass 0.02 kg moving at 200 m/s fired from a gun of mass 4 kg: recoil speed = (0.02 × 200) ÷ 4 = 1 m/s backward. In a collision, total momentum before = total momentum after. Rockets work on this principle.

Law	Statement in short	Example
First	Inertia: no net force, no change of state	Jerk in a braking bus
Second	F = ma	Pushing a trolley
Third	Equal and opposite reaction on another body	Rocket, gun recoil

Friction

Friction is the force that opposes the relative motion (or the tendency of motion) between two surfaces in contact. It acts parallel to the surfaces and is caused by surface roughness and molecular attraction.

Static friction: acts when the body is at rest; it adjusts up to a maximum called limiting friction.
Kinetic (sliding) friction: acts when one surface slides on the other; it is less than limiting friction.
Rolling friction: when a body rolls; it is much less than sliding friction, which is why wheels and ball bearings are used.
Order: limiting (static) > kinetic (sliding) > rolling.
f = μN, where μ is the coefficient of friction and N is the normal reaction. μ has no unit. Friction does not depend on the area of contact (for ordinary surfaces) but depends on the nature of surfaces and the normal force.
Example: a 10 kg block on a horizontal floor, μ = 0.3, g = 10: N = 100 N, f = 30 N.
Advantages: walking, braking, holding objects, writing, lighting a match. Disadvantages: wear and tear, loss of energy as heat.
Reducing friction: lubricants (oil, grease), ball bearings, polishing, streamlining. Increasing friction: rough surfaces, treads on tyres, spikes on shoes.
Fluid friction (drag) acts on objects moving through liquids and gases.

Pressure

Pressure = force (thrust) ÷ area; unit pascal (Pa) = N/m². Thrust is the force acting perpendicular to a surface. A sharp knife cuts better because a small area gives a large pressure; a wide tank track or a camel's broad feet reduce pressure; school bags have wide straps.
Pressure in liquids: P = hρg (depth h, density ρ). It increases with depth, acts in all directions, and depends not on the shape of the container. Dams are built thicker at the bottom. Example: depth 5 m of water (ρ = 1000, g = 10): P = 5 × 1000 × 10 = 50,000 Pa.
Pascal's law: pressure applied to a confined fluid is transmitted equally in all directions. Applications: hydraulic lift, hydraulic brake, hydraulic press. In a hydraulic lift, F₂/A₂ = F₁/A₁. A force of 100 N on a piston of area 10 cm² can balance a load of 1000 N on a piston of area 100 cm².
Atmospheric pressure: the air above exerts pressure. At sea level it is about 1.013 × 10⁵ Pa (101,325 Pa), which is called 1 atmosphere, and equals 76 cm of mercury column. Measured by a barometer (invented by Torricelli); a manometer measures gas pressure. Atmospheric pressure decreases with altitude. A falling barometer reading signals a storm. Examples of atmospheric pressure: drinking through a straw, suction cups, a dropper.
Other units: 1 bar = 10⁵ Pa; 1 atm ≈ 1.013 bar.

Gravitation

Universal law of gravitation: every body attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

F = G m₁m₂ / r², where G = 6.67 × 10⁻¹¹ N m²/kg² (universal gravitational constant, found by Cavendish). The force is attractive, acts along the line joining the bodies, and obeys Newton's third law. Doubling the distance reduces the force to one fourth.

Acceleration due to gravity: g = GM/R² ≈ 9.8 m/s² on Earth's surface. It is greatest at the poles and least at the equator (because the Earth bulges and rotates), decreases with height above the surface and with depth below it, and is zero at the Earth's centre. g on the Moon is about one sixth of that on Earth.

Mass and weight

Mass	Weight
Quantity of matter	Force of gravity on the body, W = mg
Scalar, kg	Vector, newton
Same everywhere	Varies with g
Measured by physical balance	Measured by spring balance

A body of mass 60 kg has weight 600 N (g = 10) on Earth and about 100 N on the Moon. Weight is zero in free fall (apparent weightlessness in a satellite) but mass remains the same.

Free fall: all bodies fall with the same acceleration in vacuum. Escape velocity from Earth is about 11.2 km/s; the orbital speed of a satellite close to the Earth is about 7.9 km/s. A geostationary satellite orbits above the equator with a period of 24 hours and appears fixed in the sky. Kepler's laws: planets move in ellipses with the Sun at one focus; a line from Sun to planet sweeps equal areas in equal times; the square of the period is proportional to the cube of the mean distance (T² ∝ r³). The Moon's gravitational pull causes ocean tides.

Buoyancy and Archimedes' principle

A liquid exerts an upward force on a body immersed in it, called buoyant force (upthrust).
Archimedes' principle: when a body is wholly or partly immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced.
Buoyant force = V × ρ_fluid × g, where V is the volume immersed.
Apparent weight in the liquid = weight in air − buoyant force.
Density = mass ÷ volume (kg/m³); relative density = density of substance ÷ density of water (no unit). Density of water = 1000 kg/m³ = 1 g/cm³ at 4 °C.
Law of floatation: a body floats if its weight is balanced by the buoyant force; for a floating body, the weight of the liquid displaced equals the weight of the body.
Density of body < density of liquid: floats (part above the surface).
Equal: floats fully submerged, in equilibrium.
Greater: sinks.
Examples: a steel ship floats because its overall (average) density, with enclosed air, is less than water; a ship sinks deeper in fresh water than in sea water; a hydrometer measures the relative density of liquids; a lactometer tests milk; ice floats with about nine-tenths of its volume below water.
Example: a stone of volume 200 cm³ fully in water: buoyant force = 0.0002 × 1000 × 10 = 2 N. If the stone weighs 5 N in air, the apparent weight is 3 N.

Exam traps

Mass is a measure of inertia; weight is a force and varies with place.
Action and reaction are equal and opposite but do not cancel because they act on different bodies.
Friction does not depend on the area of contact; it depends on the normal force and the nature of surfaces.
Sliding friction is less than limiting friction but more than rolling friction.
G (universal constant) is not the same as g (acceleration due to gravity).
g is greater at the poles than at the equator, and it is not zero in a satellite; the body only feels weightless.
Buoyant force depends on the volume immersed and fluid density, not on the body's own density.
For a floating body the buoyant force equals its own weight; for a fully sunk body it equals the weight of the liquid displaced by the full volume, which is less than its weight.

One-liners

1. Inertia is measured by mass.
2. F = ma; 1 N = 1 kg m/s².
3. Momentum = mass × velocity.
4. Impulse = force × time = change in momentum.
5. Total momentum is conserved when no external force acts.
6. Friction f = μN.
7. Rolling friction is the smallest of the three types.
8. Pressure in a liquid P = hρg.
9. Atmospheric pressure at sea level is about 1.013 × 10⁵ Pa.
10. G = 6.67 × 10⁻¹¹ N m²/kg²; g = 9.8 m/s².
11. Escape velocity of the Earth is about 11.2 km/s.
12. Buoyant force equals the weight of the fluid displaced.

Practice questions

The first law of motion is also called the law of
1. momentum
2. action and reaction
3. inertia
4. gravitation
Answer
C. inertia
It describes the tendency of bodies to keep their state.
The measure of inertia of a body is its
1. volume
2. weight
3. velocity
4. mass
Answer
D. mass
A heavier body has greater inertia.
A passenger in a bus falls forward when the bus stops suddenly. This is due to
1. inertia of rest
2. friction
3. inertia of motion
4. gravity
Answer
C. inertia of motion
The body tends to continue moving.
The SI unit of momentum is
1. kg/m s
2. kg m/s²
3. N/m
4. kg m/s
Answer
D. kg m/s
Momentum = mass × velocity.
A force of 10 N acts on a 5 kg body. Its acceleration is
1. 0.5 m/s²
2. 50 m/s²
3. 2 m/s²
4. 15 m/s²
Answer
C. 2 m/s²
a = F/m = 10 ÷ 5 = 2 m/s².
Impulse is equal to
1. force ÷ time
2. mass × acceleration
3. change in momentum
4. change in velocity
Answer
C. change in momentum
F·t = mv − mu.
A cricketer pulls his hands back while catching a fast ball to
1. increase the force
2. reduce the mass of the ball
3. increase the momentum
4. increase the time and reduce the force
Answer
D. increase the time and reduce the force
Impulse is the same, so longer time gives smaller force.
A 2 kg ball changes its speed from 3 m/s to 8 m/s in 0.5 s. The force acting is
1. 20 N
2. 10 N
3. 40 N
4. 5 N
Answer
A. 20 N
F = m(v − u)/t = 2 × 5 ÷ 0.5 = 20 N.
A bullet of mass 0.02 kg is fired at 200 m/s from a gun of mass 4 kg. The recoil speed of the gun is
1. 0.1 m/s
2. 2 m/s
3. 10 m/s
4. 1 m/s
Answer
D. 1 m/s
Momentum conservation: 4 × v = 0.02 × 200 = 4, so v = 1 m/s.
The recoil of a gun is explained by
1. Newton's first law only
2. Newton's third law and conservation of momentum
3. Archimedes' principle
4. Pascal's law
Answer
B. Newton's third law and conservation of momentum
Equal and opposite momentum changes occur.
Action and reaction forces do not cancel each other because they
1. act at different times
2. act in the same direction
3. act on different bodies
4. are unequal
Answer
C. act on different bodies
Cancellation requires forces on the same body.
A rocket moves upward because of
1. air pressure below it
2. the reaction of the exhaust gases pushed downward
3. the pull of the Moon
4. Archimedes' principle
Answer
B. the reaction of the exhaust gases pushed downward
Third law and conservation of momentum.
The force of friction acts
1. opposite to the relative motion of the surfaces
2. in the direction of motion
3. perpendicular to the surface
4. only on liquids
Answer
A. opposite to the relative motion of the surfaces
Friction opposes relative motion or its tendency.
Which of the following is the smallest?
1. Static friction
2. Sliding friction
3. Rolling friction
4. Limiting friction
Answer
C. Rolling friction
Limiting > sliding > rolling.
The formula for friction is
1. f = μ/N
2. f = μ + N
3. f = N/μ
4. f = μN
Answer
D. f = μN
μ is the coefficient of friction; N is the normal reaction.
A 10 kg block rests on a horizontal floor with μ = 0.3 (g = 10 m/s²). The maximum friction force is
1. 3 N
2. 300 N
3. 100 N
4. 30 N
Answer
D. 30 N
N = 100 N, f = 0.3 × 100 = 30 N.
Sliding friction between two surfaces mainly depends on
1. the nature of the surfaces and the normal force
2. the area of contact only
3. the speed only
4. the colour of surfaces
Answer
A. the nature of the surfaces and the normal force
For ordinary surfaces, area has no effect.
Ball bearings are used to
1. increase weight
2. increase friction
3. reduce friction by replacing sliding with rolling
4. reduce pressure
Answer
C. reduce friction by replacing sliding with rolling
Rolling friction is much less than sliding friction.
The SI unit of pressure is
1. joule
2. pascal
3. watt
4. newton
Answer
B. pascal
1 Pa = 1 N/m².
A force of 200 N acts perpendicular on an area of 0.5 m². The pressure is
1. 400 Pa
2. 100 Pa
3. 200 Pa
4. 1000 Pa
Answer
A. 400 Pa
P = F/A = 200 ÷ 0.5 = 400 Pa.
A sharp knife cuts better than a blunt one because the sharp edge has
1. a larger area
2. less thrust
3. less force
4. a smaller area, so greater pressure
Answer
D. a smaller area, so greater pressure
For the same force, a smaller area gives more pressure.
Pressure at depth h in a liquid of density ρ is
1. ρg/h
2. hρg
3. h/ρg
4. hρ/g
Answer
B. hρg
P = hρg.
The pressure due to 5 m depth of water (ρ = 1000 kg/m³, g = 10 m/s²) is
1. 500,000 Pa
2. 500 Pa
3. 50,000 Pa
4. 5,000 Pa
Answer
C. 50,000 Pa
P = 5 × 1000 × 10 = 50,000 Pa.
Dams are built thicker at the bottom because
1. pressure of water increases with depth
2. water density is zero at the bottom
3. pressure decreases with depth
4. water is lighter at the bottom
Answer
A. pressure of water increases with depth
Deeper water exerts greater pressure.
Pascal's law is used in a
1. barometer
2. hydraulic lift
3. spring balance
4. hydrometer
Answer
B. hydraulic lift
Pressure applied to a confined fluid is transmitted equally.
In a hydraulic lift, a force of 100 N is applied on a piston of area 10 cm². The load that can be balanced on a piston of area 100 cm² is
1. 10 N
2. 100 N
3. 10,000 N
4. 1000 N
Answer
D. 1000 N
F₂ = F₁ × A₂/A₁ = 100 × 10 = 1000 N.
A barometer is used to measure
1. speed
2. relative density
3. atmospheric pressure
4. temperature
Answer
C. atmospheric pressure
The mercury barometer was invented by Torricelli.
Atmospheric pressure at sea level is equal to about
1. 76 cm of mercury
2. 760 cm of mercury
3. 7.6 cm of mercury
4. 10 cm of mercury
Answer
A. 76 cm of mercury
1 atm = 76 cm Hg ≈ 1.013 × 10⁵ Pa.
If the distance between two bodies is doubled, the gravitational force between them becomes
1. double
2. one half
3. four times
4. one fourth
Answer
D. one fourth
F ∝ 1/r², so (1/2)² = 1/4.
The value of the universal gravitational constant G is
1. 6.67 × 10¹¹ N m²/kg²
2. 6.67 × 10⁻¹¹ N m²/kg²
3. 9.8 m/s²
4. 9.8 N m²/kg²
Answer
B. 6.67 × 10⁻¹¹ N m²/kg²
G is a universal constant; 9.8 m/s² is g.
The acceleration due to gravity is greatest at the
1. top of a mountain
2. equator
3. poles
4. centre of the Earth
Answer
C. poles
The Earth is flatter at the poles and the rotation effect is zero there.
The weight of a body of mass 60 kg on Earth (g = 10 m/s²) is
1. 600 N
2. 60 N
3. 6 N
4. 6000 N
Answer
A. 600 N
W = mg = 60 × 10 = 600 N.
The mass of a body taken to the Moon will
1. become zero
2. become one sixth
3. become six times
4. remain the same
Answer
D. remain the same
Mass is constant; weight changes with g.
The escape velocity from the Earth is about
1. 9.8 km/s
2. 11.2 km/s
3. 3 km/s
4. 7.9 km/s
Answer
B. 11.2 km/s
7.9 km/s is the orbital speed near the Earth.
The buoyant force on a body immersed in a liquid is equal to
1. the density of the body
2. the volume of the liquid
3. the weight of the liquid displaced
4. the weight of the body
Answer
C. the weight of the liquid displaced
This is Archimedes' principle.
A stone of volume 200 cm³ is fully immersed in water (ρ = 1000 kg/m³, g = 10 m/s²). The buoyant force is
1. 200 N
2. 20 N
3. 2 N
4. 0.2 N
Answer
C. 2 N
0.0002 × 1000 × 10 = 2 N.
A stone weighs 5 N in air and the buoyant force on it in water is 2 N. Its apparent weight in water is
1. 3 N
2. 2 N
3. 7 N
4. 10 N
Answer
A. 3 N
Apparent weight = 5 − 2 = 3 N.
A body floats in a liquid when its density is
1. zero
2. equal to that of the Earth
3. greater than that of the liquid
4. less than that of the liquid
Answer
D. less than that of the liquid
Lower density means it displaces its own weight with less submerged volume.
A steel ship floats because its average density (with the enclosed air) is
1. zero
2. less than that of water
3. equal to steel
4. more than that of water
Answer
B. less than that of water
The hollow hull displaces a large volume of water.
The relative density of a substance is
1. density of water ÷ density of the substance
2. mass × volume
3. weight ÷ mass
4. density of the substance ÷ density of water
Answer
D. density of the substance ÷ density of water
It has no unit.
Consider the statements on friction. 1. Friction depends on the normal reaction. 2. Friction always depends strongly on the area of contact.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
For ordinary surfaces friction is independent of the area of contact.
Consider the statements on mass and weight. 1. Weight is constant everywhere. 2. Mass is constant everywhere.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Weight varies with g.
Consider the statements on Newton's laws. 1. Action and reaction act on different bodies. 2. Action and reaction cancel each other on the same body.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
They act on different bodies and do not cancel.
Consider the statements on pressure in liquids. 1. Pressure in a liquid depends mainly on the shape of the container. 2. Pressure increases with depth.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Pressure depends on depth and density, not the shape of the container.
Match the law or principle with its application. P. Pascal's law Q. Archimedes' principle R. Newton's third law S. Newton's first law
1. P-jerk in a braking bus, Q-rocket, R-ship, S-hydraulic brake
2. P-rocket, Q-jerk, R-hydraulic brake, S-ship floating
3. P-hydraulic brake, Q-ship floating, R-rocket, S-jerk in a braking bus
4. P-ship floating, Q-hydraulic brake, R-jerk in a braking bus, S-rocket
Answer
C. P-hydraulic brake, Q-ship floating, R-rocket, S-jerk in a braking bus
Standard applications of each law.

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1.The collision in which the two particles operate simultaneously after collision are called _________.
2.The building up and movement of ships is based on ________.
3.The centripetal force required to keep the moon in its orbit is provided by which force?
4.The following statement applies to which law from the given options?'The line that joins any planet to the sun sweeps equal areas in equal intervals of time.'
5.The force of attraction between two bodies which is directly proportional to the product of masses of the bodies and inversely proportional to the square of the distance of separation is ________.
6.The force of attraction between all masses in the universe, especially the attraction of the earth's mass for bodies near its surface is called ________.
7.The force of attraction applied between molecules of the same substance is called:
8.The force of friction is the speed of some object ______
9.The formula for knowing stress is:
10.The first law of motion is known as the

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