Question

A block is attached to the end of an ideal spring and moved from coordinate $x_i$ to coordinate $x_f$. The relaxed position is at $x=0$. The work done by spring is positive if.

• A. $x_i=2cm$ and $x_f=4$cm
• B. $x_i=-2$cm and $x_f=4$cm
• C. $x_i=-4$cm and $x_f=4$cm
• D. $x_i=4$cm and $x_f=-2$cm

Answer 1

The correct option is D $x_i=4$cm and $x_f=-2$cm

work done by spring is positive if change in energy stored is negative.

so $\frac{1}{2}k{x}_f^2-\frac{1}{2}k{x}_i^2$

so $|x_f|<|x_i|$.

only possible answer is option D.