Brake power is defined as the power developed by an engine at the output shaft.
Mathematically can be expressed as,
![W_b = (2\pi NT)/(60*1000)](https://img.qammunity.org/2020/formulas/physics/college/k6a9mh6sps1p3rg0p3ivzke6pr3xmc5pep.png)
Where,
T = Torque
N = Number of Revolution
Torque is defined as the force by the distance applied, that is
![T = F*d](https://img.qammunity.org/2020/formulas/physics/college/oxpdvazp4yop3dcf5wwlksp8dzi08ka5ak.png)
![T = 9000*0.075](https://img.qammunity.org/2020/formulas/physics/college/crnlq5brcorja2ohx5ygut74br62trgihp.png)
![T= 675N\cdot m](https://img.qammunity.org/2020/formulas/physics/college/sbtum6ymiu4434c2mqr2l43cgz35zu0amf.png)
The number of revolution would be
![N = (4200)/(1.2)](https://img.qammunity.org/2020/formulas/physics/college/4era65scr2dvp5mk23iyg373g4va1njbe7.png)
![N = 3500rev/min](https://img.qammunity.org/2020/formulas/physics/college/bf08rzsl5kna706voszfyy1rk5avzse0p3.png)
Finally the Brake power would be:
![W_b = (2\pi NT)/(60*1000)](https://img.qammunity.org/2020/formulas/physics/college/k6a9mh6sps1p3rg0p3ivzke6pr3xmc5pep.png)
![W_b = (2\pi (675N\cdot m)(3500rev/min))/(60*1000)](https://img.qammunity.org/2020/formulas/physics/college/1o3qfz7d5kulzjl29zixilnjvfdlp456g3.png)
![W_b = 247.4W](https://img.qammunity.org/2020/formulas/physics/college/h5le63ar9ard4xwsny74uan5lxb4dcr6nn.png)