Question

Derive an expression for h in terms of m, m, r, t and constants.

Answer 1

To derive the expression for h in terms of m, m, r, t, and constants, you need to equate the Coulomb and centripetal forces and insert an expression for velocity from the condition for angular momentum quantization. This involves relating the two radii using the expression for the center-of-mass and considering the equal but opposite momenta of the two masses. Finally, you can express a and t in terms of the masses m₁ and m₂, and g.

Step-by-step explanation:

To derive an expression for h in terms of m, m, r, t, and constants, we need to equate the Coulomb and centripetal forces and then insert an expression for velocity from the condition for angular momentum quantization.

1. Start with the relationship of the period to the circumference and speed of orbit for one of the masses.
2. Use the result of the previous problem using momenta in the expressions for the kinetic energy.
3. Relate the two radii using the expression for the center-of-mass and note that the two masses must have equal but opposite momenta.

From these steps, you can express a and t in terms of the masses m₁ and m₂, and g as follows:

a = m₂ / (m₁ + m₂)

t = r₁ + r₂

where r = r₁ + r₂.

Answer 2

To derive an expression for h in terms of m, m, r, t, and constants, you need to equate forces, use angular momentum quantization, relate radii, and utilize torque.

Step-by-step explanation:

To derive an expression for h in terms of m, m, r, t, and constants, we need to utilize the equations and information given in the question.

1. Start by equating the Coulomb force and the centripetal force, which will give you an expression for velocity. Use the condition for angular momentum quantization to find the expression for velocity.
2. Next, use the relationship of the period to the circumference and speed of orbit for one of the masses to relate the two radii r1 and r2.
3. Finally, gather terms and use torque and other rotational quantities to multiply and divide the right-hand side of the equation by r. This will give you the desired expression for h.