$A$ crew of scientists has built a new space station. The space station is shaped like a wheel of radius $R,$ with essentially all its mass $M$ at the rim. When the crew arrives,the station will be set rotating at a rate that causes an object at the rim to have radial acceleration $g,$ thereby simulating Earth's surface gravity. This is accomplished by two small rockets,each with thrust $T$ newtons,mounted on the station's rim. How long a time $t$ does one need to fire the rockets to achieve the desired condition?

• A
  $t=\frac{\sqrt{gR^3}M}{2T}$
• B
  $t=\frac{\sqrt{gR}M}{2T}$
• C
  $t=\sqrt{\frac{gR}{\pi}}\,\frac{M}{T}$
• D
  $t=\frac{\sqrt{gR}M}{\pi T}$