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  • Solve! Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm ) , about its axis be I . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is :

 Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm ) , about its axis be I . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is :

  • Option 1)

     16 cm

  • Option 2)

     18 cm

  • Option 3)

    14 cm

  • Option 4)

    12 cm

Answers (1)

best_answer

 

Radius of gyration (K) -

Radius of Gyration of a body about an axis is the effective distance from the axis where the whole mass can be assumed to be concentrated so that moment of inertia remains the same.

- wherein

I= MK^{2}

K= \sqrt{\frac{I}{M}}

I=\frac{m\left ( 20^{2}+10^{2} \right )}{2}

now let moment of interia of thin cylinder

I=mk^{2}

I=mk^{2}=m\frac{20^{2}+10^{2}}{2}

k=\sqrt{\frac{400+100}{2}}=5\sqrt{10}cm

k\approx 16cm

 


Option 1)

 16 cm

Option 2)

 18 cm

Option 3)

14 cm

Option 4)

12 cm

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