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. `-mgv_(0)t^(2)costhetahat(j)`
B. `mgv_(0)tcosthetahat(k)`
C. `-(1)/(2)mgv_(0)t^(2)costhetahat(k)`
D. `(1)/(2)mgv_(0)t^(2)costhetahat(i)`

Answer

3

Explanation

`vec(L)=vec(r)xx(m vec(v))`
`vec(r)=v_(0)cos thetat hat(i)+(v_(0)sinthetat-(1)/(2)g t^(2))hat(j)`
`vec(v)=v_(0)cos theta hat(i)+(v_(0)sintheta-g t)hat(j)`
`vec(L)=mv_(0)costhetat(-(1)/(2)g t)hat(k)`
`=-(1)/(2)mg v_(0) t^(2) costheta hat(k)`