Question

A body of mass $m$ dropped from a certain height strikes a light vertical fixed spring of stiffness k. The height of its fall before touching the spring if the maximum compression of the spring is equal to $\frac{3mg}{k}$ is

• A. $\frac{3mg}{2k}$
• B. $\frac{2mg}{k}$
• C. $\frac{3mg}{4k}$
• D. $\frac{mg}{4k}$

Answer 1

The correct option is A $\frac{3mg}{2k}$

$0.5k{x}^2=mgh$

$0.5k(3mg/k{)}^2=mgh$

$0.5\left(9m^2{g}^2/k\right)=mgh$

$h=4.5mg/k$

height of fall = $4.5$ mg/k - $3$ mg/k = $1.5$ mg/k