Explain the following concepts by doing 2 simple experiments with household items to show: (Select any one from the options)

(A) Air contracts on cooling

(B) Friction opposes motion

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Teach the concept of “Factors and Multiples”. Explain using two real-life examples.

Note: Don’t include common factors, common multiples, LCM or HCF. Only focus on factors and multiples.

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1. Define the second law of reflection.
2. Take three sticks of equal length. Assume one as an incident ray, second as normal and the third as a reflected ray. Arrange these three sticks such that it follows the first law of reflection but it does NOT follow the second law of reflection.

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In a decimal number 12.43, 12 is the whole number part and 43 is the decimal part.

Anurag solved three addition problems on decimal numbers as shown below. The method followed is also written below.

Problem I: 12.43 + 2.34 = (12+2). (43+34) = 14.77

Method followed: He added whole number parts separately and decimal parts separately as shown above and put the decimal in between resultant whole number part and decimal part.

Now, he followed the same method (followed in the problem I) for problem II and problem III as shown below.

Problem II: 1.12+2.5 = (1+2). (12+5) = 3.17

Problem III: 2.56 + 1.62 = (2+1). (56+62) = 3.118

The teacher said that the answers for the Problem II and problem III are wrong.

Now, answer the following questions. (Hint: use place value)

(a) Why did the above method fail for Problem II, but gave the correct answer for Problem I. Explain the reasoning behind it?

(b) Why did the above method fail for Problem III?

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Comment on the following statements in the context of circular motion.

1. Is it possible to have a non-uniform motion that is periodic?
2. Is it possible to have a uniform motion that is non-periodic?

If you think the above statements are true, then walk around a circular path of any suitable radius to demonstrate the above motions i.e. non-uniform periodic motion and uniform non-periodic motion. (Please note that uniform motion implies constant speed)

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You have to construct a quadrilateral ABCD. In which of the following cases can you draw a unique quadrilateral.

Draw a rough sketch for each case on a page or whiteboard and explain why are you able/unable to draw a unique quadrilateral in given cases.

Case I: AB = 5 cm, AD = 7 cm, ∠DAB = 70° and ∠ABC = 120°

Case II: AB = 6 cm, BC = 5 cm, CD = 8 cm, AD = 7 cm and ∠ABC = 60°

Case III: AB || CD, AB = 6 cm, BC = 7 cm ∠ABC = 70° and ∠DAB = 80°

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