Question

An object of mass $ m $ falls on to a spring of constant $k$ from height $ h. $ The spring undergoes compression by a length $ x. $ The maximum compression $ x $ is given by the equation:

• A. $m g h=\frac{1}{2} k x^{2}$
• B. $m g(h+x)=\frac{1}{2} k x^{2}$
• C. $ m\,g(h+x)=-kx $
• D. $ m\,g\,h=-kx $

Answer 1

Answer: (B)

Energy is conserved. From law of conservation of energy potential energy at height $h=$ energy stored in compressed spring.
$\therefore m g h+m g x=\frac{1}{2} k x^{2} $
$\Rightarrow m g(h+x)=\frac{1}{2} k x^{2}$