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. `L`, only if `v_(0)=omega_(0)r`
B. greater than `L`, if `v_(0)gt omega_(0)r`
C. less than, `L` if `v_(0)gt omega_(0)r`
D. `L`, for all value of `v_(0)` and `omega_(0)`

Answer

D

Explanation

`L=RxxMv_(0)+Iomega_(0),=Mv_(0)r+Iomega`, which is constant