The spring is initially in unstretched condition. It is first stretched by a length ' x ' and the work done is W₁ . Then again it is stretched by further length ' x ' when the work done is W₂ . The value of W₂ is given by

Step-by-step solution

Work done in stretching a spring from its natural length to an extension x is given by W₁ = 1 2 kx^2 . When the spring is further stretched by a length x , the total extension becomes 2x . Total work done from the natural length to an extension 2x is W = 1 2 k(2x)^2 = 4 ( 1 2 kx^2 ) = 4W₁ . Work done in the second step is W₂ = W - W₁ = 4W₁ - W₁ = 3W₁ . Answer: 3W₁