Question

A force `overset rarr(F) = alpha hati + 3 hatj + 6 hatk` is acting at a point `overset rarr(r ) = 2 hati - 6 hatj - 12 hatk`. The value of `alpha` for which angular momentum about origin is conserved is
A. `1`
B. `-1`
C. `2`
D. zero

Answer 1

Correct Answer - B
Angular momentum, `L =` constant, when
`overset rarr(tau) = overset rarr(r ) xx overset rarr(F) = 0`
i.e. `(2hati - 6hatj - 12 hatk) xx (alpha hati + 3hatj + 6hatk) = 0`
or `|[hati,hatj,hatk],[2,-6,-12],[alpha,3,6]|= 0`, which gives `alpha = - 1`