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

`vec(tau)=vec(A)xxvec(L)` when `A` is constant vector. Accroding to given condition, it is cross product so `vec(tau)` is perpendicular to `vec(L)` and also to `vec(A)`. Forther more `|(dl)/(dt)|=Al sin theta` the component `vecL` in the direction of `vec(A)`(i.e, `lcos theta`) will not change which time. otherwise `AL sin theta` will not satishfied. The magnitude of `vec(L)` does not change becose `Avec(L)` is perpendicular to `vec(tau)`