A particle of mass `m=5 kg` is moving with a uniform speed `v=3 sqrt(2)` 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. `40 sqrt2` units
C. Zero
D. `7.5` units

Explanation

`vecL = vecr xx vecp`
`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 the
`y = mx + c`
`m = tan theta = 1 implies theta = 45 ^(@)`
`angle OQP= angle OPQ = 45 ^(@)`
Length of the `bot ar`
`= OR = OP sin 45 ^(@)`
`= ( 4)/(sqrt2) =2 sqrt2`
Angular momentum of particle along this line
`= r xx mv = 2 sqrt2 xx 5 xx 3 sqrt2 =60` units.