GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

A steel spur pinion has a module (m) of $1.25\mathit{m}\mathit{m},20$ teeth and ${20}^{\circ }$ pressure angle. The pinion rotates at 1200 rpm and transmits power to a 60 teeth gear. The face width (F) is $50\mathit{m}\mathit{m}$, Lewis form factor $\mathit{Y}=0.322$ and a dynamic factor $\mathit{K}\mathit{v}=1.26.$ The bending stress ( $\mathit{\sigma }$ ) induced in a tooth can be calculated by using the Lewis formula given below. If the maximum bending stress experienced by the pinion is $400\mathit{M}\mathit{P}\mathit{a}$, the power transmitted is ____________kW (round off to one decimal place).
Lewis formula: $\mathit{\sigma }=\frac{{\mathit{k}}_{\mathit{v}}{\mathit{W}}^{\mathit{t}}}{\mathit{F}\mathit{m}}$, where ${\mathit{W}}^{\mathit{t}}$ is the tangential load acting on the pinion.