The x component of the angular momentum of a particle whose position vector is r with components x,y and z and linear momentum is p with components `p_(x),p_(y)` and `p_(z)` is

Options

A. `xp_(y)-yp-(x)`
B. `yp_(z)-zp_(y)`
C. `zp_(x)-xp_(z)`
D. `xp_(y)+yp_(x)`

Answer

B

Explanation

We know that , `r=xhat(i) +yhat(j)+zhat(k)`
`p=p_(x)hat(i)+p_(y)hat(j)+p_(z)hat(k)`
Let `L=L_(x)hat(i)+L_(y)hat(j)+L_(z)hat(k)` .....(i)
As `L=rxxp=|{:(hati,hatj,hatk),(x,y,z),(p_x,p_y,p_z):}|=hat(i)(yp_(z)-zp_(y))+hat(j)(zp_(x)-xp_(z))+hat(k)(xp_(y)-yp_(x))...(ii)`
Comparing the coefficients of `hat(i)hat(j) and hat(k)` in Eqs.(i) and (ii) , we get `{:(L_x,hatj,hatk),(x,y,z),(p_x,p_y,p_z):}`