= Solution
Write the lost <mass> fraction as $f$, with $f=0.02$, and let $\mu=GM$. Initially the <circular orbit> has $v_0^2=\mu/R$, zero radial <velocity>, and specific <angular momentum> $h^2=R^2v_0^2=\mu R$. The stipulated rapid symmetric loss leaves the satellite's instantaneous position and <velocity> unchanged, but reduces the gravitational parameter to $\mu'=(1-f)\mu$. There is no impulsive kick from contact with ejecta in this model.
The new specific orbital <energy> is
$$
\varepsilon'=\frac{v_0^2}{2}-\frac{\mu'}R
=\frac\mu R\left(f-\frac12\right),
$$
and $h$ remains unchanged because the post-loss <force> is still central. At a radial turning point,
$$
\varepsilon'=\frac{h^2}{2r^2}-\frac{\mu'}r.
$$
Inserting the known constants and factoring yields
$$
(1-2f)r^2-2(1-f)Rr+R^2
=(r-R)\bigl[(1-2f)r-R\bigr]=0.
$$
For $0<f<1/2$ the two radii are $R$ and $R/(1-2f)$. The initial radius is the <pericentre>: immediately after the loss, $\ddot r=h^2/R^3-\mu'/R^2=f\mu/R^2>0$, so the satellite begins moving outward. Therefore
$$
\boxed{r_{\min}=R,\qquad r_{\max}=\frac R{0.96}=\frac{25}{24}R.}
$$
Equivalently, the new <semi-major axis> is $49R/48$ and the <orbital eccentricity> is $1/49$. These values also satisfy $r_{\min}=a(1-e)$ and $r_{\max}=a(1+e)$. For loss of half the original <mass> the ideal trajectory becomes parabolic, and larger loss makes it unbound. Slow adiabatic loss would give a different, nearly circular expansion; it is not the instantaneous limit stipulated here.
\Image[/past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2014-resit-orbit-after-mass-loss.png]
{title=Original <effective potential> comparison and turning radii after an instantaneous two-percent central <mass> loss}
The figure retains the same <angular momentum> before and after the change. Once the expelled material is far away, a spherically symmetric outer shell exerts no interior gravitational <force> by the <shell theorem>; direct ejecta interaction and the shell's finite transit time are neglected as in the source idealization.
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