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Rule #3

The probability of event A AND event Boccurring is the probability of event A times the probability of event B given that event Ahas already occurred.

Example: Joseph rolls two fair, six-sided

die. What is the probability that bothdie will roll a 6?

Probability of 1st die coming up 6: 1/6

Probability of 2nd die coming up 6: 1/6Probability of both die coming up 6: (1/6) *

(1/6)

Probability of both die coming up 6: 1/36

Rule #4

The probability of event A OR event Boccurring is the probability of event A

occurring plus the probability of event Boccurring minus the probability of both

events occurring.Example: Charles rolls a fair, six-sided die.

What is the probability of Charles rolling a

2 or a 4?

Probability of 2: 1/6Probability of 4: 1/6

Probability of a 2 or 4: 1/6 + 1/6

Probability of a 2 or 4: 2/6Probability of a 2 or 4: 1/3

SOLVED QUESTIONSA certain deck of cards contains 2 blue cards,

2 red cards, 2 yellow cards, and 2 green

cards. If two cards are randomly drawn fromthe deck, what is the probability that they

will both are not blue?

ANS B 1/4

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Introduction to hooke's law experiment

The Hooke's law of elasticity states that "Within the elastic limit, the extension or

compression (deformation) of an elastic material is directly proportional to the axial loadapplied". Mathematically, Hooke's law can be represented as:

F = -k x

x is the displacement of the end of the string from its equilibrium position

F is the force applied on the material; and

k is the force constant (or spring constant).

Applications of Hooke's Law Experiment

Hooke's law is used to determine the yield point of a material. This is

crucial for selecting materials which will subjected to heavy loads.Examples of its application include designing springs for shock absorbers

and dampening vibrations in machines.

Hooke's Law Experiment

Aim: To determine the force constant (k) of a given spring.

Materials required: Vertical spring stand, elastic spring, standard

attachable weights, pointer attachable to the end of the spring, hook

attachable to the spring with a pan to hold weights, ruler.

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Procedure:

1. Suspend the spring from the spring stand.

2. Attach the pointer and the hook with the pan to the end of the of the

spring.

3. Place the ruler vertically (on a vertical stand if required) such that thepointer corresponds to a readable marking on the ruler.

4. Note the initial reading of the pointer against the ruler.

5. Place a known weight on the pan.

6. Note the displacement x of the pointer.

7. Repeat steps 5 and 6 with different weights (3 trials).

8. For each case, calculate the force constant k using the formula k =mg/x, where m is the mass of the weight used, g = 9.8 m/s.

9. Find the average of the force constants calculated. This is the final force

constant of the spring

Precautions:

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1. Ensure that the spring does not oscillate when the reading of the pointer

is measured.

2. Ensure that there is no parallax error.

It is clear from Galileo's experiments that all objects have a tendency to continue in theirstate of rest or of uniform motion until an external force acts on it. The following

examples will help to understand the observations of Galileo's experiment.

Place a cardboard on an empty tumbler and a coin on the cardboard as shown in the

figure.

Cardboard and a Coin placed on an Empty Tumbler

Flick the cardboard with the finger. What do you observe? The coin drops into thetumbler. When we flick the cardboard the cardboard moves fast whereas the coin

continues in its state of rest and hence drops into the tumbler.

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Coin Drops into the Tumbler as the Cardboard is Flicked

A passenger standing in a moving bus leans forward when the brakes are applied all of a

sudden. This is because the body of the passenger is in motion along with the bus. Whenthe bus stops all of a sudden, the lower part of his body comes to rest along with the bus

whereas the upper part of the body continues to move forward.

From the above examples it is clear that objects continue to remain in their state of rest or

of uniform motion until an external force is applied. This tendency of an object to resist

any change in its state of rest or of uniform motion is called inertia.

Inertia can be defined as the property of matter by virtue of which it opposes any change

in its state of rest or of uniform motion along a straight line.

Inertia is Classified as:

Inertia of rest

Inertia of motion

Inertia of direction

Examples of Inertia of Rest A passenger standing in a bus leans backwards when the bus starts all of a sudden

Fruits fall down when the branches of a tree are shaken

Dust particles on a carpet falls when we beat the carpet with a stick

Examples of Inertia of Motion

A passenger standing in a moving bus leans forward when the bus stops all of a

sudden

A man carelessly alighting from a moving train leans forward

Example of Inertia of Direction

The water particles sticking to the cycle tyre are found to fly off tangentially

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Whenever a driver is negotiating a curve, the passengers experience a force acting

away from the centre of the curve

Inertia of a body depends upon its mass. That is, massive objects possess more inertiathan lighter ones.