Torque developed by a motor while running at 1000 rpm is 106 N-m and the shaft torque available is 100 N-m. then the iron and mechanical losses in watts are:

Correct option is A

​$$\text{The difference between the developed torque and the shaft torque accounts for the iron and mechanical losses.} \\[10pt]\textbf{Given:} \\[6pt]\bullet \ \text{Developed torque } T_d = 106 \, \text{N}\cdot\text{m} \\[4pt]\bullet \ \text{Shaft torque } T_{sh} = 100 \, \text{N}\cdot\text{m} \\[4pt]\bullet \ \text{Speed } N = 1000 \, \text{rpm} \\[14pt]\textbf{Torque corresponding to losses:} \\[8pt]T_{\text{loss}} = T_d - T_{sh} = 106 - 100 = 6 \, \text{N}\cdot\text{m} \\[14pt]\textbf{Angular speed:} \\[8pt]\omega = \frac{2\pi N}{60} = \frac{2\pi \times 1000}{60} = \frac{100\pi}{3} \, \text{rad/s} \\[14pt]\textbf{Iron and mechanical losses (power):} \\[8pt]P_{\text{loss}} = T_{\text{loss}} \times \omega = 6 \times \frac{100\pi}{3} = 200\pi \, \text{}$$​​