Question

A spring of spring constant K = 15 N/m is cut into two parts of ratio of length 3 : 1. Find the spring constant of spring with smaller length (in N/m).

• A. 60
• B. 40
• C. 30
• D. 70

Hint:

A common mistake is to think that the spring constant is directly proportional to the length. Always remember that for a spring made of a uniform material, cutting it makes it stiffer. A shorter spring has a larger spring constant.

Answer 1

The Correct Option is A

To find the spring constant of the smaller piece of the spring, we need to understand the concept that when a spring is cut into parts, the spring constant of each part is inversely proportional to its length. Let's solve this step-by-step:

1. The original spring constant of the uncut spring is \( K = 15 \, \text{N/m} \).
2. The spring is cut into two parts with a ratio of lengths \( 3:1 \). Let's denote the total length of the original spring as \( L \). Therefore, the lengths of the two parts are as follows:

• Length of the longer part \( = \frac{3}{4} L \)
• Length of the shorter part \( = \frac{1}{4} L \)

1. According to the principle mentioned earlier, the spring constant \( K' \) of a part is given by:

\(K' = \frac{K}{\text{fraction of length of the part}}.\)

1. Therefore, the spring constant of the shorter part, which has a length fraction of \( \frac{1}{4} \), is calculated as:

\(K_{\text{short}} = \frac{15}{\frac{1}{4}} = 15 \times 4 = 60 \, \text{N/m}.\)

1. Hence, the spring constant of the spring with the smaller length is \( 60 \, \text{N/m} \).

Thus, the correct answer is 60.