`M.I.` of a uniform horizontal solid cylinder of mass `M` about an axis passing through its edge and perpendicular to the axis of cylinder when its length is `6` times of its radius `R` is

Options

A. `39MR^(2)/4`
B. `39MR/4`
C. `49MR/4`
D. `49MR^(2)/4`

Answer

D

Explanation

Moment of inertial, `I = (ML^(2))/(3)+(MR^(2))/(4)`
but, L = 6 R
`M = (M 36 R^(2))/(3)+(MR^(2))/(4)`
`= 12 MR^(2)+(MR^(2))/(4)`
`= (48 MR^(2))+(MR^(2))/(4)`
`therefore I = (49)/(4) MR^(2)`.