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Q.

Consider a gyroscope, in which a uniform disc of radius R = 5.0 cm at the end of a light rod of length l=10cm  is mounted on the floor of an elevator going up with a constant acceleration a=6 m/s2 . The other end of the rod is hinged at O. Plane of the disc is perpendicular to rod. Let mass of the disc is 200 grams and mass of rod and friction are to be neglected. The disc has angular velocity ω  about the rod, and the rod-disc system (gyroscope) is precessing about vertical axis passing through O at rate n = 0.5 rps. Then   Take g = 9.8 m/s2

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a

ω=400    rad/s approximately

b

n is proportional to  l

c

Rate of change of  ω vector is proportional to torque about O

d

Precession frequency decreases when torque about O increases

answer is A, B, C.

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Detailed Solution

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mgl×dωdt=I×ω×ω1 ω1=2πn=π,  So   ω1=g1lπR2n=4×102  rad/s

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