Question

A massless spring gets elongated by amount \( x_1 \) under a tension of 5 N. Its elongation is \( x_2 \) under the tension of 7 N. For the elongation of \( 5x_1 - 2x_2 \), the tension in the spring will be:

• A. 15 N
• B. 20 N
• C. 11 N
• D. 39 N

Hint:

The elongation of a spring is directly proportional to the applied force, so use the proportionality constant to find the tension for any given elongation.

Answer 1

The Correct Option is C

The elongation of a spring is directly proportional to the applied tension (according to Hooke's law), so we can write: \[ x_1 = k \cdot 5, \quad x_2 = k \cdot 7, \] where \( k \) is the spring constant. Now, for the elongation \( 5x_1 - 2x_2 \), we have: \[ 5x_1 - 2x_2 = 5(k \cdot 5) - 2(k \cdot 7) = k(25 - 14) = k \cdot 11. \] The tension required for this elongation is \( T = k \cdot 11 \), so the tension is 11 N.