Question

Im absence of torque the frequency changes from 1 to 16 the ratio of radius of gyration

Answer 1

since torque is equal to zero .

using conservation of linear momentum :

A x a = B x b

where,

A = initial moment of inertia($MK^{2} _{1}$)

(here K1 = initial radius of gyration )

a = initial angular velocity(2$\pi$f1)

(here f 1 = initial frequency)

B = final moment of inertia($MK_{2} ^{2}$)

b = final angular velocity(2$\pi$f2)

Putting values we get ratio of radius of gyration equal to 4