Question

In most paramagnetic materials, the individual magnetic particles have more than two independent states (orientations). The number of independent states depends on the particle's angular momentum “quantum number” j, which must be a multiple of 1/2. For j = 1/2 there are just two independent states, as discussed in the text above and in Section 3.3. More generally, the allowed values of the z component of a particle's magnetic moment are

Short answer

The expression of Newton's law of motion is as follows,

Here is the mass of the object and is the acceleration of the object.

Free body diagram of the Rocket is as follows,

Step-by-step solution

Step 1. Given.

Apply the Newton's second law of motion along -axis.

Rearrange the above expression for

From the free body diagram of rocket, the expression of net force along -axis is as follows, (there is only thrust and gravitational force along -axis)

Combine the above expression of net force along -axis and the expression of acceleration along -axis,

Step 2. Given.

Rearrange the derived expression of acceleration (in part a.) to find the mass of the rocket,

Further solve, to find the expression for mass,

Substitute for for and for in the above expression of mass, the mass of rocket remains is as follows,