Question

A block of mass $5\text{kg}$ is dropped on a vertical spring of spring constant $1200\text{N/m}$ from a height of $10\text{m}$. Assuming that all the energy of the block is absorbed by the spring, what is the compression produced in the spring?
(Take $g=10{\text{m/s}}^2$)

• A. $9.12\text{m}$
• B. $912\text{mm}$
• C. $9.12\text{mm}$
• D. $11.2\text{cm}$

Answer 1

The correct option is B $912\text{mm}$

Initial potential energy of the block $=mgh$
This potential energy is converted into spring potential energy when the block hits the spring.
i.e $mgh=\frac{1}{2}k{x}^2$,
where $x=$ displacement produced in the spring.

$\Rightarrow 5\times 10\times 10=\frac{1}{2}\times 1200\times x^2$
$\Rightarrow \frac{1000}{1200}=x^2$
$\Rightarrow x=0.912\text{m}=912\text{mm}$