Question

Two identical blocks each of mass $m$ being interconnected by a light spring of stiffness $k$ is pushed by a force $F$ as shown in the figure. The maximum potential energy stored in the spring is equal to:

• A. $\frac{F^2}{2K}$
• B. $\frac{F^2}{4K}$
• C. $\frac{F^2}{8K}$
• D. none of these

Answer 1

The correct option is A $\frac{F^2}{2K}$

Max. PE will be stored when the compression of the spring is max. and this will occur when rhe second box is just about to move.

Now, compression just before box starts moving $=x=\frac{F}{k}$

$\Rightarrow$ PE stored=$0.5\times k\times x^2=\frac{F^2}{2k}$

Hence correct answer is option $A$