Two torsion pendula (P, Q) are shown. They differ only by the addition of cylindrical masses. The radius of each additional mass is 14th of the radius of the disc. If each cylinder and disc have equal mass, then
A
moment of inertia of Q is 1627MR2
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B
moment of inertia of Q is 2716MR2
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C
ratio of periods of P and Q is (34)12
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D
ratio of periods of P and Q is (23)32
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Solution
The correct options are B moment of inertia of Q is 2716MR2 C ratio of periods of P and Q is (23)32 I1θ+Aθ=0 I2θ+Aθ=0 where A is restoring coefficient of each time ω1=√AI1 ω2=√AI2 I1=MR22 I1=MR22+2[M2(R4)2+M(3R4)2]=2716MR2 Ratio of periods, T1T2=ω2ω1=√I1I2 ⇒T1T2=(23)32