-
A particle of mass m = 5 is moving with a uniform speed v = 3√2 in the XOY plane along the line y = x + 4. The magnitude of the angular momentum of the particle about the origin is
-
- 60 units
- units
- zero
- 7.5 units
Correct Option: A
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 straight line
y = mx + c
m = tan θ = 1
⇒ θ = 45°
∠OQP = ∠OPQ = 45°
If we draw a line perpendicular to this line,
length of the perpendicular = OR
In ∆OPR, OR/OP = sin 45°
⇒ OR = OP sin 45°
| = 4 × | = | = 2√2 | ||
| √2 | √2 |
Angular momentum of particle going along
this line = r × mv = 2√2 × 5 × 3√2 = 60 units
