Question

k is the force constant of a spring what will be the work done in increasing its extension form ℓ₁ to ℓ₂ be ? 

(A) k (ℓ – ℓ₂) 

(B) (k/2) (ℓ₂ + ℓ₁) 

(C) k (ℓ₂² + ℓ₁²) 

(D) (k/2) (ℓ₂² – ℓ₁²)

Answer 1

Correct option: (D) (k/2) (ℓ₂² – ℓ₁²)

Explanation:

At extension ℓ₁, stored energy = (1/2) kℓ₁² 

At extension ℓ₂, stored energy = (1/2) kℓ₂² 

Workdone in increasing extension from ℓ₁ to ℓ₂ = (1/2) k(ℓ₂² – ℓ₁²)