Question

In the given figure `F=10N, R=1m`, mass of the body is `2kg` and moment of inertia of the body about an axis passing through `O` and perpendicular to the plane of the body is `4kgm^(2)`. `O` is the centre of mass of the body.
If the ground is smooth, what is the total kinetic energy of the body after `2s`?
A. `100J`
B. `75J`
C. `50 J`
D. `25J`

Answer 1

Correct Answer - C
(A) When frictional force is absent, rigid body does not translate.
`sum vec(F)` external =0, therefore `vec(a)CM=0`, Taking torque about `CM`
`Fxx2R-FxxRI_(CM)alpha`
`10xx1=4alpha`
`alpha=5/2 rad//sec^(2)`
`omega=alphat=5 rad//sec^(2)`
`KE_("total")=1/2I_(CM)omega^(2)=1/2xx4xx5xx5=50 J`
(B) Taking torque about `IC`
`Fxx4R-Fxx3R=[I_(CM)+M(2R)^(2)]alpha`
`10xx1=[4+2xx(2xx1)^(2)]alpha`
`alpha=10/12 rad//sec^(2)`
`omega=alphat=10/12xx2=5/3 rad//sec`
`ke_("total")=1/2[I_(CM)+M(2R)^(2)]omega^(2)`
`=1/2[4+2xx(2xx1)^(2)](5/3)^(2)`
`16.67 J`