Question

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

Answer 1

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

\[\text{ Original length of rope L = 2 m} \]
\[\text{ Extension in the rope ∆ L = 0 . 01 m }\]
\[\text{ Area of cross - section of the rope A }= 2 \times {10}^{- 4} \]
\[\text{ We know that }: \]
\[\text{ Young's modulus Y }= \frac{F}{A} \times \frac{L}{∆ L}\]
\[ = \frac{100}{2 \times {10}^{- 4}} \times \frac{2}{0 . 01}\]
\[ \Rightarrow Y = 1 \times {10}^8 \text{ N/ m}^2\]

Hence, the required Young's modulus  for the rope is \[1 \times {10}^8 \text{ N/ m}^2\] .