Answer:
The correct option is;
c. 12.8 cm
Step-by-step explanation:
The given parameters are;
The length of each spring = 12 m = 0.12 m
Given that the masses and the springs are vertically oriented, we have;
The mass on the first spring = 3 × 6.4 = 19.2 kg
The weight on the first spring = 19.2 kg × 9.81 m/s² = 188.352 N
The extension of the first spring = 188.352 N/7,800 N/m ≈ 0.02415 m
The mass on the second spring = 2 × 6.4 = 12.8 kg
The weight on the second spring = 12.8 kg × 9.81 m/s² = 125.568 N
The extension of the second spring = 125.568 N/7,800 N/m ≈ 0.016098 m
The mass on the third spring = 1 × 6.4 = 6.4 kg
The weight on the third spring = 6.4 kg × 9.81 m/s² = 62.784 N
The extension of the third (bottom) spring = 62.784 N/7,800 N/m ≈ 0.00805 m
The total length of the bottom spring = Original length of the bottom spring + Extension of the bottom spring
The total length of the bottom spring ≈ 0.12 m + 0.00805 m = 0.12805 m
The total length of the bottom spring ≈ 0.12805 m ≈ 12.81 cm
The bottom spring will be approximately 12.81 cm long.