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JEE Main 2025 (23 Jan, Shift 1) · Other SHM Systems

Other SHM Systems question from JEE Main 2025 (23 Jan, Shift 1)

Q8JEE Main 2025 · 23 JAN · SHIFT 1Medium

Other SHM Systems

A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ×10−2 sy\pi \times 10^{-2}\text{ s}, where the value of yy is (Acceleration due to gravity, g=10 m/s2g = 10\text{ m/s}^2, density of water =103 kg/m3= 10^{3}\text{ kg/m}^3)

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Answer: (a)

  1. T=2πmρAgT = 2\pi\sqrt{\frac{m}{\rho A g}} with m=0.01 kgm = 0.01\text{ kg}, A=0.01 m2A = 0.01\text{ m}^2.
  2. T=2π0.01103×0.01×10=2π×10−2 sT = 2\pi\sqrt{\frac{0.01}{10^3 \times 0.01 \times 10}} = 2\pi \times 10^{-2}\text{ s}
  3. So y=2y = 2, answer (a).
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