Two point-like objects of masses 20 g m and 30 g m are fixed at the two ends of a rigid massless rod of length 10 c m . This system is suspended vertically from a rigid ceiling using a thin wire attac

Question

Two point-like objects of masses 20 g m and 30 g m are fixed at the two ends of a rigid massless rod of length 10 c m . This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1.2 × 1 0 − 8 N m r a d − 1 . The angular frequency of the oscillations is n × 1 0 − 3 r a d s − 1 . The value of n is ____ .

TestHub · Accepted Answer

Centre of mass is 6 cm from the 20 g mass; $I = 0.02 (0.06)^{2} + 0.03 (0.04)^{2} = 1.2 \times 1 0^{- 4} kg m^{2}$ .

$ω = \frac{κ}{I} = \frac{1.2 \times 1 0 ^{- 8}}{1.2 \times 1 0 ^{- 4}} = 1 0^{- 2} = 10 \times 1 0^{- 3} rad / s$

So $n = 10$ .

Answer: 10

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