Consider a particle of mass m having linear momentum `vecp` at position `vecr` relative to the origin O. Let `vecL` be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate(s) `vecr`, `vecp` and `vecL`?A. `(dvecL)/(dt) + vecr xx (dvecp)/(dt)=0`B. `(dvecL)/(dt) + (dvecr)/(dt) xx vecp=0`C. `(dvecL)/(dt) - (dvecr)/(dt) xx vecp=0`D. `(dvecL)/(dt)- vecr xx (dvecp)/(dt)=0`

Consider a particle of mass m having linear momentum `vecp` at positio

1.	Consider a particle of mass m having linear momentum `vecp` at position `vecr` relative to the origin O. Let `vecL` be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate(s) `vecr`, `vecp` and `vecL`?A. `(dvecL)/(dt) + vecr xx (dvecp)/(dt)=0`B. `(dvecL)/(dt) + (dvecr)/(dt) xx vecp=0`C. `(dvecL)/(dt) - (dvecr)/(dt) xx vecp=0`D. `(dvecL)/(dt)- vecr xx (dvecp)/(dt)=0`
Answer» Correct Answer - d As `vecL= vecr xx vecp` Differentiate both sides with respect to time, we get `(dvecL)/(dt) - d/(dt) (vecr xx vecp) = (dvecr)/(dt) xx vecp + vecr xx (dvecp)/(dt)` `=vecr xx (dvecp)/(dt)` `therefore (dvecr)/(dt) xx vecp=0` `(dvecL)/(dt) - vecr xx (dvecp)/(dt)=0`

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