Question

Natural length of a massless spring (of spring constant $k$) is $x$. It is slowly stretched by applying an external force. What is the work done in slowly increasing its extension from $3x$ to $4x$?

• A. $1.5k{x}^2$
• B. $2.5k{x}^2$
• C. $-3.5k{x}^2$
• D. $3.5k{x}^2$

Answer 1

The correct option is D $3.5k{x}^2$

It is given in the problem that,
Initial displacement $=3x$ and Final displacement $=4x$
So, work done by external force is given by
$W=\frac{1}{2}(k{x}_f^2-k{x}_i^2)$
$W=\frac{1}{2}k{x}^2(16-9)$
$W=3.5k{x}^2$
Therefore, work done by the external force is,
$W=3.5k{x}^2$