Simple Machines

Question 1:

Classify the following as a lever, a pulley and an inclined plane :
A wedge, a needle, a staircase, a slide, the wheel of a flagpole, nutcrackers, scissors, an opener, an axe, a crane, a knife.

ANSWER:

A wedge: An inclined plane
A needle: An inclined plane
A staircase: An inclined plane
A slide: An inclined plane
The wheel of a flagpole: A pulley
Nutcrackers: A lever
Scissors: A lever
An opener: A lever
An axe: An inclined plane
A crane: A pulley
A knife: An inclined plane

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Question 2:

Fill in the blanks using the proper word and complete the statements.
(a) The ....... in the centre, the .......... on one side and the ...... on the other side make a lever of the first order.
(b) The ..... in the centre, the ........ on one side and the ......... on the other side make a lever of the second order.
(c) The .......... in the centre, the ....... on one side and the........on the other side make a lever of the third order.

ANSWER:

(a) The fulcrum in the centre, the load on one side and the effort on the other side make a lever of the first order.
(b) The load in the centre, the fulcrum on one side and the effort on the other side make a lever of the second order.
(c) The effort in the centre, the load on one side and the fulcrum on the other side make a lever of the third order.

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Question 3:

Which machines will you use to do the following work? Write their types.
(a) To remove the lid of a tin.
(b) To lift bricks to the top of a tall building.
(c) To cut vegetables.
(d) To draw water from a well.
(e) To hold a papad for roasting it.

ANSWER:

(a) To remove the lid of a tin, we should use an opener which is a second order lever.

(b) To lift bricks to the top of a tall building, we should use a crane which is a pulley.

(c) To cut vegetables, we should use a knife which is a wedge.

(d) To draw water from a well, we should use a pulley system or wheel-axle.

(e) To hold a papad for roasting it, we should use a tong which is a third order lever.

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Question 4:

Write the answers to the following questions in your own words.
(a) What is meant by simple machines?
(b) Mention the advantages of using a machine.
(c) What is meant by complex machines?
(d) What is a lever ? How are the orders of the lever determined?

ANSWER:

(a) Simple machines are the tools that help people work faster and better. These help us lift heavy loads, change the speed of the motion or the direction of force. Examples are simple machines are knife, nutcrackers etc.

(b) The advantages of using a machine are:

• More work can be done in lesser time as well as with great accuracy
• Less effort has to be applied to accomplish the task

(c) A machine made up of two or more simple machines is called a complex machine. It consists of different parts that carry out different task and together contribute to the working of the machine. The most common example is that of a bicycle.

(d) A lever is a simple machine consisting of a rigid rod which is capable of turning around a pivot called a fulcrum. It has three parts, namely, effort, load and fulcrum.

• Fulcrum: The rod of the lever rests on it and the lever rotates about it.
• Load: The weight lifted by the liver is called the load.
• Effort: The force applied on the other end of the rod to lift the load is called the effort.

The orders of the lever are determined depending on the position of the effort, the fulcrum and the load.
Lever of first order: When the fulcrum is situated between load and effort, we call it a lever of first order. For example, beam balance, a crowbar, a see-saw.

Lever of second order: When the fulcrum and effort are situated at the two opposite ends of the lever and a load is placed in between them, we call it a lever of second order. For example, a nutcracker, a wheel-barrow, etc.

Lever of third order: When the fulcrum and load is situated at the opposite ends of the lever and an effort is applied somewhere between them, we call it a lever of third order. For example, a pair of tongs, a fishing rod, etc.

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Question 5:

Why is this so?
(a) Traveller’s bags have wheels.
(b) Machines have to be maintained.
(c) A bicyle is said to be a complex machine.

ANSWER:

(a) Traveller's bag has wheels so that it can be dragged easily because of reduced friction between the ground and the wheel. Thus, the wheel, a simple machine, helps to decrease the effort to be applied on the load which is a bag here.

(b) A machine is composed of many parts. These parts rub against one another when in use. Due to this, these parts wear out with time. Also, soil and dust creates more friction between the parts which further deteriorates their condition. Even, some parts get affected by weather and thus rust and erode. Because of these factors, the machine can become useless if proper care is not given to it. So, it is very necessary that we have proper equipments and methods for the maintenance of machines. Thus, machines should be sent for maintenance check at fixed interval of time to ensure their proper working.

(c) A bicycle is composed of many simple machines, such as a screw, wheel and axle, lever, pulley, which carry out different task and together contribute to its working. Thus, the bicycle is said to be a complex machine.

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Question 6:

Name the levers mentioned in the following passage. Identify the fulcrum, load and effort of each and say which type of lever it is.
Ravi and Savita sit on a sea-saw in a garden. In the mean time, a gardener is trimming trees in the garden. He puts the leaves and other garbage in the wheelbarrow. Later, Ravi gets thirsty and he buys lemon sherbet. The sherbet seller cuts the lemon and squeezes it using a lemon squeezer. He puts small pieces of ice in the glass with the help of the tongs

ANSWER:

Levers mentioned in the passage are:
(a) Sea-saw: It is a first order lever.

(b) Wheel barrow: It is a second order lever.

(c) Lemon squeezer: It is a second order lever.

Credit:www.meritnation.com

Substances in the surroundings-their states and properties .

Question 1:

In the paragraph below, write ‘solid’, ‘liquid’ or ‘gas’ in each of the brackets depending on the substance referred to just before.
On a bright sunny day, Riya and Gargi are playing with a ball (   ) in the park. Gargi feels thirsty. So, Riya brings tender coconut water (   ) for her. At the same time, a strong breeze (   ) starts blowing and it also begins to rain (   ). They run back into the house (   ), change their clothes (   ) and then their mother gives them a cup (   ) of hot milk (   ) to drink.

ANSWER:

On a bright sunny day, Riya and Gargi are playing with a ball (solid) in the park. Gargi feels thirsty. So, Riya brings tender coconut water (liquid) for her. At the same time, a strong breeze (gas) starts blowing and it also begins to rain (liquid). They run back into the house (solid), change their clothes (solid) and then their mother gives them a cup (solid) of hot milk (liquid) to drink.

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Question 2:

Discuss.
(a) Riya pours some water from her bottle into another bottle. Does it change the shape of the water ?
(b) Halima picks up a small stone from the ground and puts it in the water in a dish. Does the shape of the stone change ?

ANSWER:

a. Yes, the shape of the water will change because liquids do not have a shape of their own. They take the shape of the container in which they are present.

b. No, the shape of the stone will not change by putting it in a dish containing water because solids have definite shape. They do not change their shape and retain it, no matter whatever be the circumstances.

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Question 3:

Write the properties of these substances.
Water, glass, chalk, iron ball, sugar, salt, flour, coal, soil, pen, ink, soap.

ANSWER:

Water- Fluidity
Glass- Transparent, brittle
Chalk- Brittle
Iron ball- Hardness
Sugar- Solubility
Salt- Solubility
Flour-Solubility
Coal- Brittle
Soil- Solubility
Pen- Hard
Ink- Fluidity
Soap- Brittle

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Question 4:

What is sublimation? Write the names of everyday substances that sublimate.

ANSWER:

Sublimation is the change of the gaseous state directly into the solid state, without going through the liquid state, and vice versa. 
Examples of sublimation:- dry ice, moth balls or napthalene balls, camphor (kapur).

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Question 5:

What is it made from? Why?
(a) A sickle to cut sugarcane.
(b) The sheets used for roofing.
(c) A screwdriver
(d) A pair of tongs.
(e) Electric cables.
(f) Ornaments.
(g) Pots and pans.

ANSWER:

(a) A sickle to cut sugarcane- Made out of iron since it is very hard and strong.
(b) The sheets used for roofing- Aluminium is used to make sheets for roofing because it is malleable i.e. it can be hammered into sheets.
(c) A screwdriver- It is made up of steel beacuse it is very hard and duable.
(d) A pair of tongs- They are made up of metals like iron or aluminium beacuse they have high melting points and do not melt while using on flames.
(e) Electric cables- Metals like silver, gold, copper and platinum are used to make wires because they are ductile i.e. they can be drawn into wires.
(f) Ornaments- Metals such as gold and silver are used for making jewellery because they are very lustrous. 
(g) Pots and pans- Copper is used to make pots and pans because it is a good conductor of heat.
 

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Question 6:

What will happen if....? And why ?
(a) Nails are made of plastic.
(b) A bell is made of wood.
(c) Rubber is not fitted on a pair of tongs.
(d) A knife is made of wood.
(e) An axe is made of rubber.

ANSWER:

a. If nails are made out of plastic, they cannot be used for its usual purposes. They could not be hammered like iron nails and ould not possess the strength which iron nails have. It means they would have no strength to hold the things together.

b. If a bell is made of wood, it will not ring. The bells are made up of metals like copper etc. as they show the property of sonority i.e. the ability to produce a ringing sound when striked upon. Wood does not have this property and hence cannot be used to make bells.

c. Tongs are made up of metals and they have the ability to conduct heat. If rubber is attached to the tongs, the heat will be transfered to the rubber and it will melt off.

d. Knife is used to cut vegetables, fruits etc. The regular knifes which we use are made up of metals like iron etc. as they are hard, strong and durable. Also they can be sharpened and moulded into shapes which we desire. Knifes made out of wood cannot be used for cutting or chopping purposes.

e. An axe is used to cut and chop wood. It is made up of metals beacause they are stong, hard and durable. Also they can be moulded and sharpened which is an important characteristic. These properties are not applicable to rubber. An axe made of rubber will neither be hard nor sharp enough so that it can be used for its usual purposes.

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Question 7:

Who am I ?
(a) I’m found in a thermometer, I measure your temperature.
(b) I make things hot or cold.
(c) I have no shape whatsoever !
(d) I dissolve in water, but not in kerosene.

ANSWER:

(a) I’m found in a thermometer, I measure your temperature- Mercury
(b) I make things hot or cold- Temperature
(c) I have no shape whatsoever !- Gas
(d) I dissolve in water, but not in kerosene- Salt

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Question 8:

Why does this happen ?
(a) Coconut oil thickens in winter.
(b) Kerosene left open in a dish disappears.
(c) The fragrance of incense sticks lighted in one corner of a room spreads to the other corner.
(d) What you see in the picture.

ANSWER:

a. Coconut oil is made up of two types of fat- saturated and unsaturated fats. It contains 90% saturated fats and 10% unsaturated fats. It remains liquid at higher temperatures but turns into solid as the temperatures drop in winters. This property of coconut oil is attributed to the higher content of saturated fats. Oils like mustard oil, sunflower oil remain liquid even in winters because they contain less amount of saturated fats as compared to coconut oil.

b. Kerosene left open in a dish disappears because it is a volatile compound. It quickly evopurates if it is kept in open.

c. When the incense stick is lighted, it releases smoke which contains the fragrance. Smoke is a form of gas which quickly spreads in the entire room along with the fragrance and thus making the entire room fragrant.

d. The picture shows two things which are present in tub of water. One is a balloon which floats on the surface of the water while the other is an apple which sinks to the bottom of the tub. The balloon floats on the surface of the water because it has less denity as compared to the density of the water whereas the apple sinks to the bottom of the tub because it has more density than water.

Algebraic Expressions

1.Classify the following algebraic expressions as monomials, binomials, trinomials or  polynomials.

(i) 7x  (ii) 5y −$-$ 7z (iii) 3x³ −$-$5x² −$-$11    (iv) 1 −$-$8a−$-$7a ²−$-$7a³

(v) 5m−$-$3 (vi) a (vii) 4

(viii) 3y²−$-$7y + 5

ANSWER:

It is known that, expressions with one term is called monomial, expressions with two terms are binomials, expressions with three terms are trinomials and expression with more than three terms are polynomials.
(i) 7x = Monomial
(ii) 5y−$-$7z = Binomial
(iii) 3x³−$-$5x²−$-$11 = Trinomial
(iv) 1−$-$8a−$-$7a²−$-$7a³ = Polynomial
(v) 5m−$-$3 = Binomial
(vi) 4 = Monomial
(vii) 3y²−$-$7y+5 = Trinomial

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Question 1:

Add.

(i) 9p + 16q ; 13p + 2q       (ii) 2a + 6b + 8c; 16a + 13c+ 18b  
(iii) 13x²−$-$12y² ; 6x² −$-$ 8y²        (iv) 17a² b² + 16c ; 28c −$-$ 28a² b²
(v) 3y² −$-$ 10y + 16 ; 2y−$-$7 ​       (vi) −$-$3y² + 10y  −$-$16 ; 7y² + 8

 

 

ANSWER:

(i) (9p + 16q) + (13p + 2q)
= 9p + 16q + 13p + 2q
=(9p + 13p) + (16q + 2q)
=22p + 18q

(ii) (2a + 6b + 8c) + (16a + 13c + 18b)
= 2a + 6b + 8c + 16a + 13c + 18b
= (2a + 16a) + (6b + 18b) + (8c + 13c)
= 18a + 24b + 21c

(iii) (13x² − 12y²) + (6x² − 8y²)
= 13x² − 12y² + 6x² − 8y²
= (13x² + 6x²) + (−12y² − 8y²)
=19x² + (−20y²)
=19x² − 20y²

(iv) (17a²b² + 16c) + (28c − 28a²b²)
= 17a²b² + 16c + 28c − 28a²b²
= (17a²b² − 28a²b²) + (16c + 28c)
= −11a²b² + 44c

(v) (3y² − 10y + 16) + (2y − 7)
= 3y² − 10y + 16 + 2y − 7
= 3y² + (−10y + 2y) + (16 − 7)
=3y² + (−8y) + 9
=3y² − 8y + 9

(vi) (−3y² + 10y − 16) + (7y² + 8)
= −3y² + 10y − 16 + 7y² + 8
= (−3y² + 7y²) + 10y  + (−16 + 8)
= 4y² + 10y + (−8)
= 4y² + 10y − 8

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Question 1:

Subtract the second expression from the first.

(i)  (4xy−9z) ; (3xy −16z) (ii)  (5x + 4y + 7z) ; (x + 2y + 3z)

(iii) (14x² + 8xy + 3y² ) ; (26x² − 8xy− 17y²)  (iv) (6x²+ 7xy+ 16y² ) ; (16x² − 17xy)

(v) (4x + 16z) ; (19y −14z + 16x)

ANSWER:

(i) (4xy − 9z) − (3xy − 16z)
= 4xy − 9z − 3xy + 16z
= (4xy − 3xy) + (16z − 9z)
= xy + 7z

(ii) (5x + 4y + 7z) − (x + 2y + 3z)
= 5x + 4y + 7z − x − 2y − 3z
= (5x − x) + (4y − 2y) + ( 7z − 3z)
= 4x + 2y + 4z

(iii) (14x² + 8xy + 3y²) − (26x² − 8xy − 17y²)
= 14x² + 8xy + 3y² − 26x² + 8xy + 17y²
= (14x² − 26x²) + (8xy + 8xy) + (3y² + 17y²)
= −12x² + 16xy + 20y²

(iv) (6x²+ 7xy+ 16y² ) − (16x² −$-$ 17xy)
= 6x² + 7xy + 16y² − 16x² +17xy
= (6x² − 16x²) + (7xy + 17xy) + 16y²
= −10x² + 24xy + 16y²

(v) (4x + 16z) − (19y − 14z + 16x)
= 4x + 16z − 19y + 14z − 16x
= (4x − 16x) + (16z + 14z) − 19y
= −12x + 30z − 19y

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Question 1:

Multiply.

(i) 16xy × 18xy (ii) 23xy² × 4yz² 

(iii) (12a + 17b) × 4c  (iv) (4x + 5y) × (9x + 7y)

ANSWER:

(i) 16xy × 18xy
= 16 × 18 × x × y × x × y
= 288x²y²

(ii) 23xy² × 4yz²
= 23 × 4 × x × y² × y × z²
= 92xy³z²

(iii) (12a + 17b) × 4c
= 12a × 4c + 17b × 4c
= 12 × 4 × a × c + 17 × 4 × b × c
= 48ac + 68bc

(iv) (4x + 5y) × (9x + 7y)
= 4x(9x + 7y) + 5y(9x + 7y)
= 4x × 9x + 4x × 7y + 5y × 9x + 5y × 7y
= 36x² + 28xy + 45xy + 35y²
= 36x² + 73xy +35y²

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Question 2:

A rectangle is (8x + 5) cm long and (5x + 3) cm broad. Find its area.

ANSWER:

Length of the rectangle = (8x + 5) cm
Breadth of the rectangle = (5x + 3) cm
Area of rectangle = length × breadth
= (8x + 5)(5x + 3)
= 8x(5x + 3) + 5(5x + 3)
= 8x × 5x + 8x × 3 + 5 × 5x + 5 × 3
= 40x² + 24x + 25x + 15
= 40x² + 49x + 15
So, area of rectangle is (40x² + 49x + 15) cm².

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Question 1:

Simplify (3x −11y)−(17x  + 13y) and choose the right answer.

 

(i) 7x −12y  (ii) −14x −$-$54y (iii) −3 (5x  + 4y )     (iv) −2 (7x + 12y )

ANSWER:

(3x − 11y) −(17x  + 13y)
= 3x −11y −17x −13y
= (3x − 17x) + (−11y −13y)
= −$-$14x + (−24y)
= −14x − 24y
= −2(7x + 12y)
So, the correct option is (iv).
 

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Question 2:

The product of (23 x² y³ z) and ( −15x³ yz² ) is .................... .

 

(i) −345  x⁵ y⁴ z³   (ii) 345  x² y³ z⁵   (iii) 145 x³y² z    (iv) 170 x³y² z³

ANSWER:

(23x²y³z) × (−15x³yz²)
= 23 × (−15) × x² × y³ × z × x³ × y × z²
= −345x⁵y⁴z³
So, the correct option is (i)

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Question 4:

Rakesh’s age is less than Sania’s age by 5 years. The sum of their ages is 27 years. How old are they?

ANSWER:

Let the age of Sania = x years
Then, the age of Rakesh = (x − 5) years
According to question, sum of ages of Sania and Rakesh is 27 years.
∴ x+(x−5)=27⇒x+x−5=27⇒2x−5=27⇒2x=27+5⇒2x=32⇒x=16$$\begin{gathered} \therefore x+\left(x-5\right)=27 \\ \Rightarrow x+x-5=27 \\ \Rightarrow 2x-5=27 \\ \Rightarrow 2x=27+5 \\ \Rightarrow 2x=32 \\ \Rightarrow x=16 \end{gathered}$$
So, age of Sania = x years = 16 years
age of Rakesh = (x − 5) years = (16 − 5) years = 11 years

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Question 5:

When planting a forest, the number of jambhul trees planted was greater than the number of ashoka trees by 60. If there are altogether 200 trees of these two types, how many jambhul trees were planted ?

ANSWER:

Let the number of ashoka trees planted in the forest = x
Then, the number of jambhul trees planted in the forest = x + 60
According to question, total number of ashoka and jambhul trees planted in the forest is 200.
⇒x + (x+60)=200⇒x+x+60=200⇒2x+60=200⇒2x=200−60⇒2x=140⇒x=1402⇒x=70$$\begin{gathered} \Rightarrow x + \left(x+60\right)=200 \\ \Rightarrow x+x+60=200 \\ \Rightarrow 2x+60=200 \\ \Rightarrow 2x=200-60 \\ \Rightarrow 2x=140 \\ \Rightarrow x=\frac{140}{2} \\ \Rightarrow x=70 \end{gathered}$$
Number of ashoka trees planted in the forest = x = 70
Number of jambhul trees planted in the forest = x + 60 = 70 + 60 = 130

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Question 6:

Shubhangi has twice as many 20-rupee notes as she has 50-rupee notes. Altogether,she has 2700 rupees. How many 50-rupee notes does she have ?

ANSWER:

Let the number of 50-rupee notes = x
Then, the number of 20-rupee notes = 2 × number of 50-rupee notes = 2x
Amount of 50-rupee notes = Rs(50 × x) = Rs 50x
Amount of 20-rupee notes = Rs(20 × 2x) = Rs 40x
It is given that total amount is Rs 2700.
∴ 50x+40x=2700⇒90x=2700⇒x=270090⇒x=30$$\begin{gathered} \therefore 50x+40x=2700 \\ \Rightarrow 90x=2700 \\ \Rightarrow x=\frac{2700}{90} \\ \Rightarrow x=30 \end{gathered}$$
Number of 50-rupee notes = x = 30
Number of 20-rupee notes = 2x = 2 × 30 = 60

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Question 7:

Virat made twice as many runs as Rohit. The total of their scores is 2 less than a double century. How many runs did each of them make ?

ANSWER:

Let the runs scored by Rohit = x
The, the runs scored by Virat = 2 × runs scored by Rohit = 2x
According to question, total of their scores is 2 less than a double century.
∴ x+2x=200−2⇒3x=198⇒x=1983⇒x=66$$\begin{gathered} \therefore x+2x=200-2 \\ \Rightarrow 3x=198 \\ \Rightarrow x=\frac{198}{3} \\ \Rightarrow x=66 \end{gathered}$$
So, runs scored by Rohit = x = 66
Runs scored by Virat = 2x = 2 × 66 = 132