JEE Mains · Physics · STD 11 - Oscillations
- JEE Mains 2021
- Hard
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(2 \pi \sqrt{\frac{ R }{ g }}\)
Step-by-step Solution
Detailed explanation
Force along the tunnel
\(F =-\left(\frac{ GMmr }{ R ^{3}}\right) \cos \theta\)
\(F =-\frac{ gm }{ R } x \left(\frac{ GM }{ R ^{2}}= g , r \cos \theta= x \right)\)
\(a=-\frac{g}{R} x\)
\(\omega^{2}=\frac{g}{R} \quad T=2 \pi \sqrt{\frac{R}{g}}\)
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