Two massless springs of spring constants K₁ and K₂ are connected one after the other forming a single chain, suspended vertically and a certain mass is attached to the free end. If x₁ and x₂ are their respective extensions and 'F' is their stretching force, the total extension produced is

Step-by-step solution

When springs are connected in series, the same stretching force F acts on each spring. The extension in the first spring is x₁ = F K₁ The extension in the second spring is x₂ = F K₂ The total extension produced is x = x₁ + x₂ x = F K₁ + F K₂ = F ( 1 K₁ + 1 K₂ ) Answer: F(1/K₁ + 1/K₂)