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System Of Particles And Rotational Motion

Question
CBSEENPH11026237
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The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then, its radius of gyration about a parallel axis through its centre of mass will be

  • 80 cm

  • 8 cm

  • 0.8 cm

  • 80 m

Solution

B.

8 cm

The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

From the theorem of parallel axis, the moment of inertia I is equal to

   I = ICM + M a2

where ICM is moment of inertia about the centre of mass and  'a'  the distance of axis from the centre.

    I = MK2 + M × (6)2

    M K12 = M K2 + 36 M

⇒     K12 = K2 + 36 

⇒       (10)2 = K2 + 36

⇒        K2  = 100 - 36

⇒         K2 = 64

⇒          K = 8 cm

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