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 hat(j)`
B. ` mg v_(0)t cos theta hat(k)`
C. ` -1/2 mgv_(0)t^(2) cos theta hat(k)`
D. `1/2 mg v_(0) t^(2) cos theta hat(i)`

Answer

C

Explanation

` vec(L) = m( vec ( R) xxvec(v) )`
` vec(L` = m [ v_(0) cos theta t hat(i) + ( v_(0) sin theta t - 1/2 gt^(2) ) hat (j) ] xx [ v_(0) cos theta hat (i) + ( v_(0) sin theta - gt ) hat (j) ] `
` = m v_(0) cos theta t [ -1/2 gt ] hat (k) = -1/2 mgv_(0) cos theta hat (k) `