A uniform sphere of mass `m` radius `r` and moment of inertia `I` about its centre moves along the `x`-axis as shown in Fig Its centre of mass moves with velocity `= v_(0)`, and it rotates about its centre of mass with angular velocity `=omega_(0)`. Let `vecL=(Iomega_(0)+mv_(0)r)(-k)`. The angular momentum of the body about the origin `O` is

Options

A. `vecL ` only if `v_(0)=omegar`
B. greater than `vecL`, if `v_(0)gtomega_(0)r`
C. less than `vecL`, if `v_(0)gtomega_(0)r`
D. `vecL,` for all values of `omega_(0)` and `v_(0)`

Answer

D

Explanation

`vecL=vecRxxmvecv_(0)+Ivecomega_(0)=mv_(0)+Iomega_(0)` (which is constant)