Question

Four bodies of masses 2 kg, 3 kg, 4 kg and 5 kg are placed at points A, B, C, and D respectively of a square ABCD of side 1 metre. The radius of gyration of the system about an axis passing through A and perpendicular to plane is

विकल्प

• `sqrt(8/7)` m

• `2sqrt(2)` m

• `sqrt(4/3)` m

• 4 m

Answer 1

`sqrt(8/7)` m

Explanation:

AC = `sqrt(1^2 + 1^2) = sqrt(2)` m

∴ I_A = `3 xx 1^2 + 4 xx (sqrt(2))^2  + 5 xx 1^2`

= 3 + 8 + 5

= 16 kg m² 

MK² = 16

∴ K² = `16/(2 + 3 + 4 + 5) = 16/14 = 8/7`

or K = `sqrt(8/7)` m