Question
The torque ⃗τ on a body about a given point is found to be ⃗A×⃗L where ⃗A is a constant vector and ⃗L is angular momentum of the body about that point. From this it follows that
Answer: Option A
:
A
Due to law of conservation of angular momentum, ⃗L= constant
i.e. ⃗L.⃗L = constant
or, ddt(⃗L.⃗L)=0
or, 2⃗L.d⃗Ldt=0
or, ⃗L⊥d⃗Ldt
Since τ=⃗A×⃗L
d⃗Ldt=⃗A×⃗L
i.e., d⃗Ldt must be perpendicular to ⃗A as well as ⃗L.
Further the component of ⃗L along ⃗A is ⃗A.⃗LA. Also
ddt(⃗A.⃗L)=⃗A.d⃗Ldt+⃗L.d⃗Adt=0 {∵⃗A⊥d⃗Ldtandd⃗Adt=⃗0}
or, ⃗A.⃗L = constant
i.e., ⃗A.⃗LA = x = constant
Since d⃗Ldt(orτ) is perpendicular to ⃗L, hence it cannot change magnitude of ⃗L but can surely change direction of ⃗L.
Was this answer helpful ?
:
A
Due to law of conservation of angular momentum, ⃗L= constant
i.e. ⃗L.⃗L = constant
or, ddt(⃗L.⃗L)=0
or, 2⃗L.d⃗Ldt=0
or, ⃗L⊥d⃗Ldt
Since τ=⃗A×⃗L
d⃗Ldt=⃗A×⃗L
i.e., d⃗Ldt must be perpendicular to ⃗A as well as ⃗L.
Further the component of ⃗L along ⃗A is ⃗A.⃗LA. Also
ddt(⃗A.⃗L)=⃗A.d⃗Ldt+⃗L.d⃗Adt=0 {∵⃗A⊥d⃗Ldtandd⃗Adt=⃗0}
or, ⃗A.⃗L = constant
i.e., ⃗A.⃗LA = x = constant
Since d⃗Ldt(orτ) is perpendicular to ⃗L, hence it cannot change magnitude of ⃗L but can surely change direction of ⃗L.
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution