Question

there are four springs stretched by the same mass. spring a stretches 25 cm. spring b stretches 10 cm. spring c stretches 100 cm. spring d stretches 1 cm. which spring is the weakest? a b c d

Explanation:

Step1: Hooke's Law

Hooke's Law is \(F = kx\), where \(F\) is the force (here, force due to mass \(F=mg\), same for all springs as mass \(m\) is same), \(k\) is the spring constant (stiffness), and \(x\) is the extension. Rearranging for \(k\), we get \(k=\frac{F}{x}\).

Step2: Analyze spring constant and weakness

A weaker spring has a smaller spring constant \(k\). Since \(F\) is constant (\(F = mg\)), \(k\) is inversely proportional to \(x\) (\(k\propto\frac{1}{x}\)). The spring with the largest extension \(x\) will have the smallest \(k\) (weakest spring).

Answer:

C. Spring C