An automobile engine develops 10⁵ W power when rotating at an angular speed of 900 rad/minute. The instantaneous torque delivered by the engine is
Solution:
The power developed by a rotating engine is given by the formula P = \tau \omega, where P is the power, \tau is the torque, and \omega is the angular speed.
Given:
Power P = 10⁵ W
Angular speed \omega = 900 rad/minute
First, convert the angular speed from rad/minute to rad/second:
\omega = 900 \frac{rad}{minute} \times \frac{1 minute}{60 seconds} = \frac{900}{60} rad/s = 15 rad/s
Now, use the power formula to find the torque \tau:
P = \tau \omega
\tau = \frac{P}{\omega}
\tau = \frac{10⁵ W}{15 rad/s}
\tau = \frac{100000}{15} N-m
\tau = \frac{20000}{3} N-m
\tau = \frac{2}{3} \times 10000 N-m
\tau = \frac{2}{3} \times 10⁴ N-m
Comparing this result with the given options, we find that it matches option (3).