A block of mass $m$ falls through a height $h$ on a spring of spring constant $k .$ The maximum displacement in the spring is

\frac{2 m g h}{k}

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\frac{m g}{k}

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\sqrt{\frac{2 m g h}{k}}

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None of these

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Solution

The correct option is D None of these
$\begin{matrix} \frac{1}{2} k x^{2} = m g (h + x) \Rightarrow \frac{1}{2} k x^{2} - m g x - m g h = 0 x = \frac{m g + \sqrt{m^{2} g^{2} + 2 m g k h}}{k} A n s . (D) \end{matrix}$

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A block of mass m falls through a height h on a spring of spring constant k. The maximum displacement in the spring is

The correct option is D None of these12kx2=mg(h+x)⇒12kx2−mgx−mgh=0x=mg+√m2g2+2mgkhkAns.(D)

A block of mass $m$ falls through a height $h$ on a spring of spring constant $k .$ The maximum displacement in the spring is

The correct option is D None of these
$\begin{matrix} \frac{1}{2} k x^{2} = m g (h + x) \Rightarrow \frac{1}{2} k x^{2} - m g x - m g h = 0 x = \frac{m g + \sqrt{m^{2} g^{2} + 2 m g k h}}{k} A n s . (D) \end{matrix}$