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Physics · WORK, ENERGY AND POWER

हिन्दी

A block on a frictionless horizontal table is connected to a spring of spring constant \( k \). If the work done by the spring force when the block moves from \( x = x_i \) to \( x = x_f \) is zero, then which of the following conditions must hold true?

  1. \( x_i = x_f \) only
  2. \( x_i = -x_f \)
  3. \( x_i = 0 \) and \( x_f = 0 \)
  4. \( |x_i| = |x_f| \)

Correct answer · Option 4

\( |x_i| = |x_f| \)

Explanation

Work done by the spring force is \( W_s = \frac{1}{2}k(x_i^2 - x_f^2) \). For \( W_s = 0 \), we need \( x_i^2 = x_f^2 \), which implies \( |x_i| = |x_f| \).
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