Question

A block of mass $m$ initially at rest is dropped from a height $h$ on to a spring of force constant $k$. The maximum compression in the spring is $x$ then:

• A. $mgh=\frac{1}{2}k\,{{x}^{2}}$
• B. $mg(h+x)=\frac{1}{2}k\,{{x}^{2}}$
• C. $mgh=\frac{1}{2}k\,{{(x+h)}^{2}}$
• D. $mg(h+x)=\frac{1}{2}k\,{{(x+h)}^{2}}$

Answer 1

Answer: (A)

$mgh=\frac{1}{2}k\,{{x}^{2}}$

Answer 2

Key Idea: Potential energy of block at height h is converted into potential energy of spring. When block is at height h, it has potential energy $mgh,$ which is converted into potential energy of spring to conserve energy i.e., $mgh=\frac{1}{2}k\,{{x}^{2}}$ where k is force constant of spring.