একটি তারের ইয়াং এর গুণাঙ্ক $2.1\times {10}^{11}N{m^{-}}^2$এবং ব্যাস 2mm। তারের দৈর্ঘ্য 0.5% বৃদ্ধি করতে হলে কত বল প্রয়োগ করতে হবে?

The answer given is $3.29\times {10}^{3}N$. To understand why this is correct, we can break down the problem step by step:

    
1. Young's Modulus (E): Given as $2.1\times {10}^{11}N$.
    
2. Diameter of the wire: Given as 2 mm, which needs to be converted to meters for the calculations. Thus, diameter = 0.002 m. This means that the radius (r) will be 0.001 m.
    
3. Length of wire (L): Assume it as 1 m for calculations. Therefore, the original length is L = 1 m.
    
4. Extension of the wire (ΔL): This is given as 0.5% of L, which is 0.005 m.
    
5. Calculating stress: Stress is defined as the force (F) over the area (A). The area of the wire's cross-section can be calculated using A = πr².
    
6. Calculating strain: Strain is defined as the change in length (ΔL) over the original length (L), i.e., Strain = ΔL / L = 0.005.
    
7. Using Young's Modulus (E): The relationship can be used as E = Stress / Strain, to find the force required.