37-12

This problem is a measurement problem much like the previous one, where the moving object is measured to be half as long as its rest length, that is

$$L=\frac{1}{2}L',$$

but we know that lengths are measured shorted by exactly $\gamma$, so we must have $\gamma=2$. The corresponding $\beta$ is then given by

$$\beta=\sqrt{1-\gamma^{-2}}=\sqrt{1-1/4}=\sqrt{3}/2=.8660.$$

Next, since moving clocks are judged to run more slowly by the factor $\gamma$ (see problem 4), the clock here runs slower by $\gamma=2$, that is, half as fast.