A force F=ai+3j+6k is acting at a point r=2i-6j-12k. The value of α for which angular momentum about origin is conserved is

Options

(a) 2
(b) zero
(c) 1
(d) -1

Correct Answer:

-1

Explanation:

From Newton’s second law for rotational motion,
τ = dL / dt, if L = constant then τ = 0
So, τ = r × F = 0
(2î – 6ĵ – 12k̂) × (αî + 3ĵ + 6k̂) = 0
Solving we get α = -1.