A force `vecF = alpha hati + 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. zero
B. 1
C. `-1`
D. 2

Answer

C

Explanation

For the conservation of angular momentum about origin , the torque `vectau` acting on the particle will be zero
By definition, `vectau = vecr xx vecF`
Here `vecr = 2hati - 6hatj - 12 hatk` and `vecF = alpha hati + 3hatj + 6hatk`
`therefore vectau = |{:(hati , hatj , hatk) , (2 , -6 , -12) , (alpha , 3 , 6):}|`
`= hati (-36 + 36) - hatj (12 + 12 alpha) + hatk (6 + 6 alpha)`
`=- hatj (12 + 12 alpha) + hatk (6 + 6 alpha)`
But `vectau = 0`
`therefore 12 + 12 alpha = 0 or alpha = -1` and `6 + 6 alpha = 0` and `alpha = -1`