A conical pendulum consists of a mass `M` suspended from a strong sling of length `l`. The mass executes a circle of radius `R` in a horizontal plane with speed `v`. At time `t`, the mass is at position `Rhati` and `vhatj` velocity. At time `t` the angular momentum vector of mass `M` about the point from which the string passes on the ceiling is

Options

A. `MvRhatk`
B. `Mvlhatk`
C. `Mvl[sqrt((l^2-R^2)/l)hati+R/lhatk]`
D. `-Mvl[sqrt((l^(2)-R^(2))/l)hati+R/lhatk]`

Answer

C

Explanation

From the figure in questions position vector if mass `vecr=Rhati-sqrt(l^(2)+R^(3)hatk)`
Linear moment `vecp=Mvhatj`
`vecL=vecvxxvecp`
substituting the values, we get result