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The time period of a mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

Asked in CBSE AIPMT 2003 · Spring combinations

• (1) T/4
• (2) T
• (3) T/2
• (4) 2T

Step-by-step solution

Why the other options are wrong

• (1) comes from divides the period by 4 because the spring constant is multiplied by 4; T∝1/(√k), so a fourfold stiffening halves the period
• (2) comes from assumes cutting the spring leaves its constant unchanged; a quarter-length spring stretches only a quarter as much under the same load, so k quadruples
• (4) comes from puts k in the numerator: a stiffer spring oscillates faster, so the period must fall, not rise

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