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JEE Main 2021 (26 Feb, Shift 1) · Other SHM Systems

Other SHM Systems question from JEE Main 2021 (26 Feb, Shift 1)

Q13JEE Main 2021 · 26 FEB · SHIFT 1Medium

Other SHM Systems

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

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Answer: (a)

  1. Inside the earth g′=grRg' = g\frac{r}{R}; its component along the chord is gRx\frac{g}{R}x, where xx is distance from the chord's midpoint.
  2. a=−gRx⇒T=2πRga = -\frac{g}{R}x \Rightarrow T = 2\pi\sqrt{\frac{R}{g}}, independent of the chord.
  3. So the answer is (a).
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