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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion

Suppose a tunnel is excavated across the earth (radius = R ) passing through its centre. Calculate the time a particle takes to traverse the length of the tunnel if it is thrown vertically upward along the length of the tunnel with a speed of gR .

Options

  1. A2 R g
  2. BR g
  3. C2 R g
  4. D4 R g

Correct answer

C. 2 R g

Step-by-step solution

The acceleration of a particle at a distance x from the centre of the earth inside a tunnel is given by a = - g R x . This represents simple harmonic motion (SHM) with an angular frequency = g R . The general equation for the position of a particle in SHM is: x(t) = x₀ ( t) + v₀ ( t) Let the particle be thrown from one end of the tunnel, so its initial position is x₀ = -R . It is thrown along the length of the tunnel with an initial speed v₀ = gR . Substituting these initial conditions into the equation of motion:

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