Question

An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a – 2b), the value of tension will be_____ N.

Answer 1

Correct Answer: 5

Given:

\[ 3 = K(a - \ell) \] \[ 2 = K(b - \ell) \]

Here, \( K \) represents the spring constant, and \( \ell \) denotes the natural length of the spring.

Determine the tension \( T \) for a length of \( (3a - 2b) \):
\[ T = K (3a - 2b - \ell) \]

Substitute \( a - \ell \) and \( b - \ell \) from the provided equations:
\[ T = K [3(a - \ell) - 2(b - \ell)] \]

\[ T = K \left[ 3 \left( \frac{3}{K} \right) - 2 \left( \frac{2}{K} \right) \right] \]

\[ T = K \left[ \frac{9}{K} - \frac{4}{K} \right] \]

\[ T = K \left[ \frac{5}{K} \right] = 5 \, \text{N} \]

Result:
The tension value is \( 5 \, \text{N} \).