Question

a force F= 2i+bj+3k is acting at a point having position r=8i+6j+12k.
the value of b for which angular momentum about orgin is conserved it .
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Answer 1

Answer:The value of b for which angular momentum about the origin is conserved is 3/2=1.5

Explanation:

Angular momentum about origin is said to be conserved if the torque,T(cross product of position vector,r and force,F i.e., r *F) is zero.

We know that,

torque,T=r x F

here, r=2i+bj+3k and F=8i+6j+12k

therefore,

T=$\left[\begin{array}{ccc}i&j&k\\2&b&3\\8&6&12\end{array}\right]$

=i(12b-18)-j(24-24)+k(12-8b)

=i(12b-18)+k(12-8b)

but T=0

=> 12b-18=0

=>b=3/2

and 12-8b=0

=>b=3/2