GATE Mechanical Engineering (ME) 2021 Shift 2 Solved Paper

Question : 44 of 65

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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

$√{\;{kr^{2}}/{J\;+\;mr^{2}}}$
${√{k\/ m}}$
$√{\;{kr^{2}}/{J−mr^{2}}}$
$√{\;{kr^{2}}/{J}}$

Validate

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