question_answer

A particle of mass \[\operatorname{m}= 5\] units is moving with a uniform speed \[\operatorname{v} =3\,\sqrt{2}\] m in the XOY plane along the\[\operatorname{y}=x+4\]. What will be the magnitude of the angular momentum about the origin?

A)  0 units             

B)  30 units

C)  60 units                       

D)  None of these

Correct Answer: C

Solution :

Angular momentum about origin is. \[r=\frac{\left| 0-0-4 \right|}{\sqrt{{{(1)}^{2}}+{{(-1)}^{2}}}}=2\sqrt{2}\] \[\left| L \right|=\left| r\times mv \right|\,=\,\,rmv\] \[=\left( 2\sqrt{2} \right)\times 5\times \left( 3\sqrt{2} \right)=60\,\,units\]