A small particle 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 ` t lt ( v_(0) sin theta)/(g) `, the angular momentum of the particle is
where `hat (i) , hat (j) and hat(k)` are unit vectors along `x , y and z` - axis 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`