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Physics · PYQ NEET UG 2016(2)
हिन्दीA body of mass \( m \) is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass \( m \) is slightly pulled down and released, it oscillates with a time period of \( 3 \text{ s} \). When the mass \( m \) is increased by \( 1 \text{ kg} \), the time period of oscillations becomes \( 5 \text{ s} \). The value of \( m \) in kg is
Correct answer · Option 1
\( \frac{9}{16} \)
Explanation
Using \( T = 2\pi\sqrt{\frac{m}{k}} \), we get \( \frac{T_1}{T_2} = \sqrt{\frac{m}{m+1}} \). Substituting \( T_1=3, T_2=5 \), we get \( \frac{3}{5} = \sqrt{\frac{m}{m+1}} \Rightarrow \frac{9}{25} = \frac{m}{m+1} \Rightarrow m = \frac{9}{16} \text{ kg} \).
