Question

The position of a particle is given by P = (i + 2j-k) momentum P = (3i+ 4j-2k). The angular
momentum is perpendicular to
(a) x-axis
(c) z-axis
(b) y-axis
(d) Line at equal angles to all the three axes​

Answer 1

answer : option (a) x - axis.

The position of particle is given by, r = (i + 2j - k)

and linear momentum of of particle is given as P = (3i + 4j - 2k)

we know angular momentum is the cross product of position of particle and linear momentum.

i.e., L = r × P

= (i + 2j - k) × (3i + 4j - 2k)

= {2(-2) - 4(-1)}i - {1 × (-2) -3(-1)}j + {1 × 4 - 3 × 2 }k

= (-4 + 4)i - (-2 + 3)j + (4 - 6)k

= -j - 2k

x - component of angular momentum is absent and hence, angular momentum is perpendicular to x-axis.

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