Question

A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

• A. $2\text{Mg/k}$
• B. $4\text{Mg/k}$
• C. $\text{Mg/2k}$
• D. $\text{Mg/k}$

Answer 1

The correct option is A $2\text{Mg/k}$


For the maximum extenction:
$mg{x}_{max}=\frac{1}{2}m{x}_{max}^2{x}_{max}=\frac{2mg}{k}$

Hence, for the maximum extenctionof spring wil be $\frac{2mg}{k}.$