there are four springs stretched by the same mass. spring a stretches 25 cm. spring b stretches 10 cm…

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

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

Answer

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