The torque `tau` on a body about a given point is found to be equal to `AxxL` where `A` is a constant vector, and `L` is the angular momentum of the body about that point. From this it follows that

Options

A. dL/dt is perpendicular to L at all instants of time
B. the component of L in the direction of A does not change with time
C. the magnitude of L does not change with time
D. L does not change with time

Answer

A, B, C

Explanation

`vecta =(dvecL)/(dt)`, Given that `vectau = vecA xx vecL rArr (dvecL)/(dt) = vecA xx vecL`
From the cross-product rule, `vec(dL)/vec(dt)` is always perpendicular to the plane containing `vecA` and `vecL`. By the dot product definition, `vecL . vecL = vecL`
Differentiating with respect to time, we get
`vecL. (dvecL)/(dt) + vecL.(dvecL)/(dt) = 2L(dvecL)/(dt) = 2L (dL)/(dt)`
Since, `dvecL//dt` is perpendicular to `vecL rArr (dL)/(dt) =0 rArr L` = constant.