The angular momentum of a particle relative to a certain point O varies with time as `M=a+bt^2`, where a and b are constant vectors, with `a_|_b`. Find the force moment N relative to the point O acting on the particle when the angle between the vectors N and M equals `45^@`.

Options

A. `sqrt((a)/(b))`
B. `2sqrt((a)/(b))`
C. `2bsqrt((a)/(b))`
D. `2asqrt((b)/(a))`

Answer

C

Explanation

`vectau=(dvecJ)/(dt)=(d)/(dt)(ahati+bt^(2)hatj)=2bthatj`
`cos45^(@)=(vectau.vecJ)/(tauJ)or(1)/(sqrt(2))=((2b+hatj).(ahati+bt^(2)hatj))/(2btxxsqrt(a^(2)+b^(2)t^(4)))`
or `t=sqrt((a)/(b))andvectau=2bxxsqrt((a)/(b))hatj`.