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

The Correct Option is A

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.