Question

A circular disc of mass M and radius R is connected to spring and placed on rough surface. The friction is sufficient for pure rolling. When the disc is slightly displaced and released, it executes simple harmonic motion.

The time period of oscillations of the disc

• A. depends on its radius
• B. depends on amplitude
• C. depends on its mass
• D. depends only on spring constant of spring

Answer 1

The correct option is C depends on its mass

$F-f=mafR=\frac{m{R}^2\alpha }{2}f=\frac{ma}{2}F=\frac{3ma}{2}F=3ff=\frac{F}{3}f=\frac{Kx}{3}X=acos\omega tf=\frac{KA}{3}cos\omega t\mu mg=\frac{KA}{3}A=\frac{3\mu mg}{K}$
$\therefore 0<A<\frac{3\mu mg}{K};$ for no slipping
$a=\frac{-2F}{3m}=\frac{-2Kx}{3m}T=2\pi \sqrt{\frac{3m}{2k}}$