Question

An ideal spring with spring-constant k is hung from the ceiling and a block of mass m is attached to its lower end. The mass is released with the spring initially unscratched. The maximum extension in the spring is

• A. $\frac{4mg}{k}$
  
• B. $\frac{2mg}{k}$
• C. $\frac{mg}{k}$
• D. $\frac{mg}{2k}$

Answer 1

The correct option is B $\frac{2mg}{k}$

Let the spring can have maximum extension $x$. Now, accroding to law of energy conservation we can write,

Decrease in gravitational potential energy of mass$=$increase in potential energy of spring.

$\Rightarrow mgx=\frac{1}{2}k{x}^2$

$\Rightarrow x=\frac{2mg}{k}$

Here gravitational potential energy of mass decreases as the mass moves down.