A small paricle of mass m is projected at an angle `theta` with the x-axis with an initial velocity `v_(0)` in the x-y plane as shown in the figure. At a time `tlt(v_(0)sin theta)/(g)`, the angular momentum of the particle is
where `hati, hatj and hatk` are unit vectors along x, y and z-axix respectively.

Options

A. `-mg v_(0)t^(2) cos theta hati`
B. `mgv_(0)t cos theta hatk`
C. `-1/2 mg v_(0) t^(2) cos theta hatk`
D. `1/2 mg v_(0) t^(2) cos theta hati`

Answer

C

Explanation

Angular momentum any time t
`[n(v_(0)sin theta=g t)v_(0)cos theta.t]=(mv_(0) cos theta)[v_(0) sin theta t-1//2 g t^(2)]`
`=-1/2 mg v_(0)t^(2) cos theta hatk`