Verified Solution • 2025–26 Session moderate

QJEEM23Ph1f00: JEE Main 2023 Physics - Class 11 JEEM23Ph1f00 Solution: Assume that the earth is a solid sphere of uniform density and…

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately)

(Take g = 10 m s−2 , radius of earth = 6400 km)

Multiple Choice Options

  • A 12 hours
  • B 1 hour 24 minutes
  • C 24 hours
  • D 1 hour 40 minutes

Step-by-Step Verified Solution

Gravitational acceleration at a distance of rr from centre of earth is given by

g′=gRr

Where RR is the radius of earth

So, d2rdt2=−gRr\frac{d^{2} r}{d t^{2}}=-\frac{g}{R} r

⇒T=2πRg=2π640000010\Rightarrow \quad T=2 \pi \sqrt{\frac{R}{g}}=2 \pi \sqrt{\frac{6400000}{10}}

=2π×800sec=2 \pi \times 800 \mathrm{sec}

=5024 sec=5024 ~ \mathrm{sec}

= 1 hour 24 minutes (approx.)

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