Angular momentum of a particle problem

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The problem involves two identical particles with equal but opposite momenta, requiring the demonstration that their total angular momentum is independent of the choice of origin. The relevant equation for angular momentum is L = r x p, and the sum of torques relates to the change in angular momentum over time. The attempt at a solution indicates confusion regarding how changing the origin affects the position vectors of the particles. By adjusting the origin, both position vectors change equally, which ultimately shows that the total angular momentum remains constant. Understanding this principle is key to solving the problem correctly.
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Homework Statement


Two identical particles have equal but opposite momenta, p and -p, but they are not traveling along the same line show that the total angular momentum of this system does not depend on the choice of origin.


Homework Equations


L=r x p
Sum of torque = dL/dt


The Attempt at a Solution


Do not understand the problem at all.
 
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Total angular momentum is r1xp+r2x(-p). If you change the origin, r1 changes to r1+d and r2 changes to r2+d. Conclusion?
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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