GATE 2021 Mechanical Engineering Q34

Question

Consider the system shown in the figure. A rope goes over a pulley. A mass, m, is hanging from the rope. A spring of stiffness, k, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.
The pulley radius is r and its mass moment of inertia is J. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is

Accepted Answer

$\sqrt{\frac{kr^2}{J+mr^2}}$

Answer

$\sqrt{\frac{kr^2}{J-mr^2}}$

Answer

$\sqrt{k/m}$

Answer

$\sqrt{\frac{kr^2}{J}}$