The torque T on a body about a given point is found to be equal to ( A L ) where A is constant vector, and (L ) is the angular momentum of the body about that point. From this it follows that (A) ( dL dt ) is perpendicular to L at all insta

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

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Correct answer: A. A, B, C

( E = d ~L ^ dt ) Given that ( t = A L dL dt = | A X L ) ( dL dt ) From cross-product rule, ( d L d t ) is always perpendicular to the plane containing (A ) and L By the dot product definition ( L . L =L^2 ) Differentiating with respect to time ( Z ~L dL dt + Z ~L dL dt =2 ~L dL dt ) ( 2 L d L d t =2 L d L d t ) Since ( d L d t ) is perpendicular to (L d L d t =0 L= ) constant

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