Question

Three particles of masses 1gm, 2gm & 3gm are at 1cm, 2cm, & 3cm from the axis of rotation respectively then the momentum of inertia of the system & radius of gyration of the system respectively are ______ gm $c{m}^2$ and _____cm.

• A. 63, 2.449
• B. 60, 4.5
• C. 36, 4.449
• D. 36, 2.449

Answer 1

The correct option is D 36, 2.449

$MOI=1(1{)}^2+2(2{)}^2+3(3{)}^2$
$=36gmc{m}^2$
Radius of gyration$=K$
then
$(1+2+3)K^2=36$
$K=\sqrt{6}$
$=2.449cm$