The moment of inertia of the disc used in a torsional pendulum about the suspension wire is 0.2 $k g - m^{2}$ . It oscillates with a period of 2s. Another disc is placed over the first one and the time period of the system becomes 2.5s. Find the moment of inertia of the second disc about the wire.

0.12

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0.13

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0.11

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0.07

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Solution

The correct option is C 0.11
If the torsional constant of the wire is k, then T = 2(I/k)
If one more disc is placed on top of the first disc, then the mass of the system increases and the new moment of inertia will be $I_{2} = I + 0.2$ , I is the moment of inertia of the second disc ]
T_2/T_1 = [(I + 0.2)/0.2] . Substituting the values , we get $I = 0.11 k g - m^{2}$ ]

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The moment of inertia of the disc used in a torsional pendulum about the suspension wire is 0.2 kg−m2. It oscillates with a period of 2s. Another disc is placed over the first one and the time period of the system becomes 2.5s. Find the moment of inertia of the second disc about the wire.

The moment of inertia of the disc used in a torsional pendulum about the suspension wire is 0.2 $k g - m^{2}$ . It oscillates with a period of 2s. Another disc is placed over the first one and the time period of the system becomes 2.5s. Find the moment of inertia of the second disc about the wire.