Question

A block of $4kg$ is suspended from the ceiling through a massless spring of spring constant $k=100N/m$. If $4kg$ is replaced by $8kg$, what would be the ratio of elongation in 1st case to 2nd case?

• A. $1$
• B. $2$
• C. $1.5$
• D. $0.5$

Answer 1

The correct option is D $0.5$

FBD of the block,

For equilibrium, spring force = Weight of the block
Case (1)
$k{x}_1=m_{1}g\Rightarrow x_1=\frac{m_{1}g}{k}\Rightarrow \frac{4\left(10\right)}{100}=0.4m$
Case (2)
$x_2=\frac{m_{2}g}{k}=\frac{8\left(10\right)}{100}=0.8m$

Ratio $=\frac{0.4}{0.8}=0.5$