Question

JEE MAINS PHYSICS QUESTION SEPTEMBER 2020

Answer 1

we have to find the ratio of moment of inertia about axis perpendicular to rectangular plate passing through O' & O.

solution : application : if a rectangular shape of mass m , length a and width b is given then moment of inertia about an axis passing through centre of mass which is perpendicular of its plane is given by, I = m/12 (a² + b²)

using above application,

moment of inertia about axis perpendicular to rectangular plate, I = m/12 [80² + 60²]

= m/12 [ 6400 + 3600 ]

= 10000m/12 ......(1)

moment of inertia about an axis passing through O' and perpendicular to its plane, I' = I + m[√(a² + b²)/2]² [ using parallel axis theorem ]

= 10000m/12 + m[6400/4 + 3600/4]

= 10000 [ m/12 + m/4 ]

= 10000 [ 4m/12] .......(2)

from equation (1) and (2) we get,

I/I' = 1/4

Therefore the ratio of moment of inertia is 1 : 4