Question

Two persons pull a rope towards themselves. Each person exerts a force of 100 N on the rope. Find the Young's modulus of the material of the rope if it extends in length by 1cm. Original length of the rope = 2m and the area of cross-section = 2cm².

Comments

Why didn't u take force 200 N in place of 100 N because exerting F will be perhaps 200N..could u please clear
 doubt

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Force (F) applied by two persons on the rope = 100 N

Answer 1

 Area of cross-section A = 2 cm² =2/10000 m² 

Force F =100 N Stress σ =F/A =100/(2/10000) =1000000/2 =500000 =5*10⁵ N/m² 

l=1 cm =1/100 m =0.01 m 

L =2 m 

Strain ε =l/L =0.01/2 =0.005  

Young's modulus of the material Y =σ/ε 

=5*10⁵/0.005 N/m² 

=1 x10⁸ N/m²

Answer 2

Young's modulus of the material of the rope: