A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Youngâ€™s modulus for the material of the wire.

[Take g = 10 msâˆ’2]

A. 2.4Ã—1010(Nmâˆ’2)

B. 1.5Ã—1010(Nmâˆ’2)

C. 2.4Ã—109(Nmâˆ’2)

D. 1.3Ã—1010(Nmâˆ’2)

Correct Option: Answer is A

Youngâ€™s modulus (Y) can be calculated using Hookeâ€™s Law, which is given by the formula:

Y =Stress/Strain

The strain (Îµ) is given by the formula:

Îµ =Extension/Original length

In this case, the extension is given as 0.5% of the original length, and the stress (Ïƒ) can be calculated using the formula:

Ïƒ =Force/Area

The force (F) can be calculated using the weight of the load (W):

F=mâ‹…g

where:

â€¢ m is the mass of the load (given as 1.5 kg),

â€¢ g is the acceleration due to gravity (given as 10 m/sÂ²).

The area (A) of the wire can be calculated using the formula for the area of a circle (A=Ï€r2), where r is the radius of the wire.

Once you have the stress and strain, you can substitute these values into the formula for Youngâ€™s modulus.

Letâ€™s go step by step:

1. Calculate the force (F): ï¿½=1.5â€‰kg*10â€‰m/s2 ; F=15â€‰N

2. Calculate the area (A): A =Ï€â‹…(0.2mm)2 => A =Ï€â‹…(0.0002m)2 Aâ‰ˆ1.2566Ã—10âˆ’7â€‰m2

3. Calculate the stress (Ïƒ): Ïƒ =15â€‰N/1.2566Ã—10âˆ’7 â‰ˆ1.193Ã—108â€‰N/m2

4. Calculate the strain (Îµ)=0.5%100 Îµ=0.005

5. Finally, calculate Youngâ€™s modulus (Y): Y=1.193Ã—108â€‰N/m20.005Y=0.0051.193Ã—108N/m2 Yâ‰ˆ2.386Ã—1010â€‰N/m2

A. 2.4Ã—10^10 N/mÂ²