Q96 / 180 · JIPMER 2017 · Physics

A solid cylinder is attached to a horizontal massless spring as shown in figure. If the cylinder rolls without slipping, the time period of oscillation of the cylinder is Figure

  • A
    $2 \pi \sqrt{\frac{x}{g}}$
  • B
    $2 \pi \sqrt{\frac{2 M}{3 K}}$
  • Correct answer
    C
    $2 \pi \sqrt{\frac{3 M}{8 K}}$
  • D
    $2 \pi \sqrt{\frac{3 M}{2 K}}$

Solution

Let $x$ be the extension in the spring, Then, $x=2 R \theta$ $\therefore$ Torque acting on the cylinder about point of contact, $T=F \times 2 R=-K x(2 R)=-4 R^2 K \cdot \theta$ $\therefore T=2 \pi \sqrt{\frac{I}{K e}}=2 \pi \sqrt{\frac{\frac{3}{2} M R^2}{4 R^2 K}}=2 \pi \sqrt{\frac{3 M}{8 K}}$

Hence, the correct answer is option: 'C'.

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