If a particle of mass `m` is moving with constant velocity `v` parallel to `x`-axis in `x-y` plane as shown in fig. Its angular moment with respect to origin at any time `t` will be

Options

A. `mvb hat(k)`
B. `- mvb hat(k)`
C. `mvb hat(i)`
D. `mv hat(i)`

Answer

B

Explanation

Angular momentum –
`vec(L) = vec(r) xx vec(P)= |(i,hat(j),hat(k)),(x,y,z),(p_(x),P_(y),p_(z))|`
`p_(x)= mv`
`x= vt, y=b`
`vec(L)= |(hat(i),hat(j),hat(k)),(vt,b,0),(mv,0,0)|= (vt xx 0- mvb) hat(k)`
`vec(L)= - mv b hat(k)`