A particle of mass m = 5 units is moving with a uniform speed `v = 3sqrt2` units in the XOY plane along the line Y = X + 4. The magnitude of the angular momentum of the particle about the origin is

Options

A. 60 units
B. `40sqrt2` units
C. zero
D. 7.5 units

Answer

A

Explanation

`vecL=vecrccvecp`
Y=X+ 4 line has been shown in the figure when x = 0,y = 4. So, OP = 4.
The slope of the line can be obtained by comparing with the equation of line
y=mx+c
`rArrm=tantheta=1`
`rArrtheta=45^(@)`
`angleOQP=angleOPQ=45^(@)`
If we draw a line perpendicular to this line.
Length of the perpendicular= OR
`rArrOR=OPsin45^(@)=4(1)/(sqrt2)=4/(sqrt2)=2sqrt2`
Angular momentum of particle going along this line
`=rxxmv=2sqrt2xx5xx3sqrt2=60` units