Question

A slab $S$ of mass $m$ is released from a height $h_{0}$ to the top of a spring of force constant $k$. The maximum compression $x$ of the spring is given by the equation

• A. $m g h_{0}=\frac{1}{2} k x^{2}$
• B. $m g\left(h_{0}-x\right)=\frac{1}{2} k x^{2}$
• C. $m g h_{0}=\frac{1}{2} k\left(h_{0}+x\right)^{2}$
• D. $m g\left(h_{0}+x\right)=\frac{1}{2} k x^{2}$

Answer 1

Answer: (D)

$\Delta U+\Delta K=0$
$\Rightarrow \Delta U_{g}+\Delta U_{s}+0=0$
$\Rightarrow -\left[\left(m g\left(h_{0}+x\right)\right]+\left(\frac{1}{2} k x^{2}-0\right)=\right.$
$\Rightarrow m g\left(h_{0}+x\right)=\frac{1}{2} k x^{2}$