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

A force vecF = alpha hati + 3hatj + 6hatk is acting at a point vecr =

1.	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
Answer» zero 1 `-1` 2 Solution :For the conservation of angular MOMENTUM about origin , the TORQUE `vectau` ACTING on the PARTICLE will be zero By definition, `vectau = vecrxx 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`