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

A uniform plate of mass M rests horizontally and symmetrically on two wheels that rotate in opposite directions, as shown in the figure. The distance between the wheels is L , and the coefficient of friction between the plate and each wheel is . Determine the time period of oscillation of the plate if it is given a slight displacement along its length and then released.

Options

  1. AL 2 g
  2. B2 L g
  3. C2 L 2 g
  4. D2 2 L g

Correct answer

C. 2 L 2 g

Step-by-step solution

Let the center of mass (CM) of the plate be displaced by a distance x towards the right from its equilibrium position. The distance of the CM from the left wheel becomes L 2 + x and from the right wheel becomes L 2 - x . Let N₁ and N₂ be the normal reactions from the left and right wheels, respectively. For vertical equilibrium: N₁ + N₂ = Mg For rotational equilibrium about the CM, the net torque is zero: N₁ ( L 2 + x ) = N₂ ( L 2 - x ) Solving these two equations, we get: N₁ = Mg L ( L 2 - x ) and N₂ = Mg L ( L 2

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