Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is 1 × 10¹¹ N m⁻². Original length of the wire is 2 m and the area of cross section is 2 cm². The wire will extend in length by _________ μ m.

Solution

Physics sir · 3 steps

Both people pull with 200 N, but the tension in the wire is just 200 N, not 400 N.

1. Find the tension. Each end is pulled with 200 N in opposite directions, so the wire is in equilibrium. The tension at every section is T = 200 N. One person's pull only balances the other's, the same as tying one end to a wall.

   Δ L = (T L)/(A Y)

2. Put in numbers. Convert the area first: A = 2 cm² = 2 × 10⁻⁴ m². Then Δ L = (200 × 2)/(2 × 10⁻⁴ × 1 × 10¹¹) = 400/(2 × 10⁷) = 2 × 10⁻⁵ m.
3. So. Δ L = 2 × 10⁻⁵ m = 20 μm, so the answer is 20.

The common slip: 40. Adding the two pulls and taking the tension as 400 N gives 40, not 20.

The idea to keep. A rope or wire pulled by equal forces at both ends carries a tension equal to one of those forces. The two pulls do not add up.

Answer from the NTA final answer key. Solution by PrepWiser.