1.62 Move the factor outside the radical in the expression $(a-1) \sqrt{-\frac{1}{a-1}}$ inside the radical, then the original expression equals
(A) $\sqrt{1-a}$.
(B) $-\sqrt{1-a}$.
(C) $\sqrt{a-1}$.
(D) $-\sqrt{a-1}$.
(China Jilin Province Seven Cities and Prefectures Junior High School Mathematics Competition, 1984)
[Solution] From the given condition, if the square root is meaningful, then $a-1<0$, thus
$$
\begin{array}{c}
a-1=-\sqrt{(a-1)^{2}}, \\
\therefore \quad \text { the original expression }=-\sqrt{-(a-1)^{2} \frac{1}{a-1}}=-\sqrt{1-a} .
\end{array}
$$

Therefore, the correct choice is $(B)$.