$27\mathrm{.}31-$ A thin, $50\mathrm{.}0-cm-$long metal bar with mass $750$ g rests on$,$ but is not attached to$,$ two metallic supports in a uniform $0\mathrm{.}450$ T magnetic field, as shown in Fig. E$27\mathrm{.}31$ A battery and a $25\mathrm{.}0$ resistor in series are connected to the supports. $($a$)$ What is the highest voltage the battery can have without breaking the circuit at the supports? $($b$)$ The battery voltage has the maximum value calculated in part $($a$).$ If the resistor suddenly gets partially short$-$circuited, decreasing its resistance to $2\mathrm{.}0,$ find the initial acceleration of the bar.

Figure E$27\mathrm{.}31$

$27\mathrm{.}31-$ A thin, $50\mathrm{.}0-cm-$long metal bar with mass $750$ g rests on$,$ but is not attached to$,$ two metallic supports in a uniform $0\mathrm{.}450$ T magnetic field, as shown in Fig. E$27\mathrm{.}31$ A battery and a $25\mathrm{.}0$ resistor in series are connected to the supports. $($a$)$ What is the highest voltage the battery can have without breaking the circuit at the supports? $($b$)$ The battery voltage has the maximum value calculated in part $($a$).$ If the resistor suddenly gets partially short$-$circuited, decreasing its resistance to $2\mathrm{.}0,$ find the initial acceleration of the bar.

Figure E$27\mathrm{.}31$