Question

Activity 3.
Roll and Push
Make a ramp. Support 1 end of the ramp so that it is 10 cm above the floor. Cut
the top and one side of a milk carton. Place it 10 cm from the end of the ramp with
the open side down and the end is facing the ramp. Using a chalk, draw a line
along the closed end of the carton. Hold a ball at the top of the ramp and release
it. Measure how far the carton moves across the floor. Repeat the procedure by
raising the ramp to 20 cm, 30 cm and 40 cm above the floor.
Table 1. Distance of movement of the carton in different elevation.
Height of the ramp
Distance of carton movement (cm)
Score
4​

Answer 1

Answer:

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Answer 2

Explanation:

Question : Prove that√5 is irrational.

Answer :

Let us assume that √5 is a rational number.

Sp it t can be expressed in the form p/q where p,q are co-prime integers and q≠0

⇒√5=p/q

On squaring both the sides we get,

⇒5=p²/q²

⇒5q²=p² —————–(i)

p²/5= q²

So 5 divides p

p is a multiple of 5

⇒p=5m

⇒p²=25m² ————-(ii)

From equations (i) and (ii), we get,

5q²=25m²

⇒q²=5m²

⇒q² is a multiple of 5

⇒q is a multiple of 5

Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√5 is an irrational number

Hence proved