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Physics · PYQ NEET UG 2025

हिन्दी

A bob of heavy mass \( m \) is suspended by a light string of length \( l \). The bob is given a horizontal velocity \( v_0 \) as shown in figure. If the string gets slack at some point \( P \) making an angle \( \theta \) from the horizontal, the ratio of the speed \( v \) of the bob at point \( P \) to its initial speed \( v_0 \) is:

  1. \( (\sin\theta)^{1/2} \)
  2. \( (\frac{1}{2 + 3\sin\theta})^{1/2} \)
  3. \( (\frac{\cos\theta}{2 + 3\sin\theta})^{1/2} \)
  4. \( (\frac{\sin\theta}{2 + 3\sin\theta})^{1/2} \)

Correct answer · Option 2

\( (\frac{1}{2 + 3\sin\theta})^{1/2} \)

Explanation

Using conservation of mechanical energy and the condition for string slackness (\( T = 0 \implies mg\sin\theta = \frac{mv^2}{l} \)), the ratio is obtained as \( (\frac{1}{2+3\sin\theta})^{1/2} \).
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