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

\(\sqrt{\frac{kr^2}{J + mr^2}}\)

\(\sqrt{\frac{kr^2}{J - mr^2}}\)

Consider the system shown in the figure. A rope goes over a pulley. A

1.	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
A.	\(\sqrt{\frac{kr^2}{J + mr^2}}\)
B.	\(\sqrt{k/m}\)
C.	\(\sqrt{\frac{kr^2}{J - mr^2}}\)
D.	\(\sqrt{\frac{kr^2}{J }}\)
Answer» B. \(\sqrt{k/m}\)