Question

A particle of mass m = 5 unit is moving with a uniform speed v = 3`sqrt2` unit in the XY-plane along the line y = x + 4. The magnitude of the angular momentum about origin is ______.

पर्याय

• zero

• 60 unit

• 7.5 unit

• 40`sqrt2` unit

Answer 1

A particle of mass m = 5 unit is moving with a uniform speed v = 3`sqrt2` unit in the XY-plane along the line y = x + 4. The magnitude of the angular momentum about origin is 60 unit.

Explanation:

Momentum of the particle

= mass × velocity

= (5) × `(3sqrt2)` = 15`sqrt2`

The direction of momentum in the XOY plane is given by

y = x + 4 

Slope of the line = 1 = tanθ

i.e., θ = 45°

Intercept of its straight line = 4

Length of the perpendicular z from the origin of the straight line
= 4 sin 45° = `4/sqrt2` = 2`sqrt2`

Angular momentum = momentum × perpendicular length

= 15`sqrt2` ​× 2 `sqrt2` ​= 60 unit