Question

The natural length of massless spring is x
(spring constant k), is slowly stretched by
applying an external force. The work done to
stretch the spring from length 3x to 4x is
(1) 1.5kx²
2 )2.5kx²
(3) 4kx²
(4) kx²​

Answer 1

Given : The natural length of massless spring is x

( spring constant k ), is slowly stretched by

applying an external force.

To find : The work done to stretch the spring from length 3x to 4x.

solution : From Work - energy theorem,

work done to stretch the spring from x₁ to x₂ = difference in potential energies

⇒W = 1/2 kx₂² - 1/2 kx₁²

= 1/2 k (4x)² - 1/2 k (3x)²

= 1/2 k × 16x² - 1/2 k × 9x²

= 8kx² - 4.5 kx²

= 3.5 kx²

Therefore work done to stretch the spring from 3x to 4x would be 3.5 kx²