A particle of mass 1 kg is moving along the line y = x + 2 (here x and y are in metres) with speed 2 m/s. The magnitude of angular momentum of particle about its origin is

Options

A. `4 kg m^(2) s^(-1)`
B. `2 sqrt2 kg m^(2) s^(-1)`
C. `4 sqrt2 kg m^(2) s^(-1)`
D. `2 kg m^(2) s^(-1)`

Answer

B

Explanation

The given eqn. of the line is `y = x + 2`
At x = -2 , y = 0 and at x = 0 , y = 2
The line is drawn as shown in the figure .
Length of perpendicular drawn from origin to this line is
`ON = r_(1) = (0 + 0 + 2)/(sqrt(1 ^(2) + 1^(2)) = sqrt2`

Angular momentum of particle about `L = m vr_(bot) = (1) (2) sqrt2 = 2 sqrt2 kg m^(2) s^(-1)`