a spring supporting a mass of 30 kg compresses 0.6 m. how far does the spring compress when it supports a…

Explanation:

Step1: Use Hooke's Law proportion

According to Hooke's Law, force $F = kx$ (where $F$ is force, $k$ is spring - constant, $x$ is compression). Force is $F = mg$ (where $m$ is mass and $g$ is gravitational acceleration). Since $k$ is constant, we have $\frac{F_1}{x_1}=\frac{F_2}{x_2}$, or $\frac{m_1g}{x_1}=\frac{m_2g}{x_2}$, which simplifies to $\frac{m_1}{x_1}=\frac{m_2}{x_2}$.

Step2: Substitute values

Given $m_1 = 30$ kg, $x_1=0.6$ m, $m_2 = 10$ kg. Substitute into $\frac{m_1}{x_1}=\frac{m_2}{x_2}$, we get $\frac{30}{0.6}=\frac{10}{x_2}$.

Step3: Solve for $x_2$

Cross - multiply: $30x_2=10\times0.6$. Then $30x_2 = 6$. Divide both sides by 30: $x_2=\frac{6}{30}=0.2$ m.

Answer:

B. 0.2 m