A force `vecF=alphahati+3hatj+6hatk` is acting at a point `vecr=2hati-6hatj-12hatk`. The value of `alpha` for which angular momentum about origin is conserved is:

Options

A. 1
B. `-1`
C. 2
D. zero

Answer

B

Explanation

Angular momentum
`vecL=`constant
`implies`torque`vectau=0`
`impliesvecrxxvecF=0`
`|(hati,hatj,hatk),(2,-6,-12),(alpha,3,6)|=0` ltBrgt `implies(-36+36)hati-(12+12alpha)hatj+(6+6alpha)hatk=0`
`implies 0 hati-12(1+alpha)hatj+6(1+alpha)hatk=0`
`-12(1+alpha)=0`
`alpha=-1`