Question:
Two springs of spring constants $ k_1 $ and $ k_2 $ are joined together in series combination. The spring constant of the combination is
Two springs of spring constants $ k_1 $ and $ k_2 $ are joined together in series combination. The spring constant of the combination is
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When springs are connected in series, the total spring constant is less than the spring constants of individual springs.
Updated On: Apr 15, 2025
- \( k_1 + k_2 \)
- \( \frac{k_1 + k_2}{2} \)
- \( \frac{k_1 k_2}{k_1 + k_2} \)
- \( \frac{k_1 + k_2}{k_1 k_2} \)
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The Correct Option is C
Solution and Explanation
Understanding the series combination of springs.
For springs in series, the total spring constant \( k_{\text{total}} \) is
given by:
\[ \frac{1}{k_{\text{total}}} = \frac{1}{k_1} + \frac{1}{k_2} \] Thus, the combined spring constant is: \[ k_{\text{total}} = \frac{k_1 k_2}{k_1 + k_2} \] Thus, the correct answer is
(C) \( \frac{k_1 k_2}{k_1 + k_2} \)
.
For springs in series, the total spring constant \( k_{\text{total}} \) is
given by:
\[ \frac{1}{k_{\text{total}}} = \frac{1}{k_1} + \frac{1}{k_2} \] Thus, the combined spring constant is: \[ k_{\text{total}} = \frac{k_1 k_2}{k_1 + k_2} \] Thus, the correct answer is
(C) \( \frac{k_1 k_2}{k_1 + k_2} \)
.
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