Question

The maximum $\text{K.E.}$ of a oscillating spring is $5\text{J}$ and its amplitude $10\text{cm}$. The force constant of the spring is:

• A. $100\text{Newton/m}$
• B. $1000\text{Newton-m}$
• C. $1000\text{Newton/m}$
• D. $1000\text{watts}$

Answer 1

The correct option is C $1000\text{Newton/m}$

Let $K$ be the force constant of the spring and $A$ be the amplitude.
From formula
${\text{(K.E.)}}_{max}=\frac{1}{2}K{A}^2$
$\Rightarrow 5=\frac{1}{2}K(10\times {10}^{-2}{)}^2$
$(\because A=10\text{cm}=10\times {10}^{-2}\text{m})$
$\Rightarrow K=\frac{10}{(10\times {10}^{-2}{)}^2}=1000\text{N/m}$
Hence, option $\left(c\right)$ is the correct answer.