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 has the smallest spring constant? a b c d

Explanation:

Step1: Recall Hooke's Law

Hooke's Law is \(F = kx\), where \(F\) is the force (here, \(F = mg\) since the mass is the same for all springs, \(m\) is mass and \(g\) is acceleration due to gravity), \(k\) is the spring - constant, and \(x\) is the extension of the spring. We can rewrite the formula for \(k\) as \(k=\frac{F}{x}\). Since \(F = mg\) is constant (same mass), \(k\propto\frac{1}{x}\) (inversely proportional to the extension \(x\)).

Step2: Compare the extensions

We are given \(x_A = 25\space cm\), \(x_B=10\space cm\), \(x_C = 100\space cm\), \(x_D = 1\space cm\).
The spring with the largest extension \(x\) will have the smallest \(k\) (because of the inverse - proportionality \(k=\frac{F}{x}\) with \(F\) constant).

Answer:

C. Spring C