Question

A rod is hinged at centre and rotated by applying the torque starting from rest ,the power developed by the torque with respect to time is of

• A. cubic nature
• B. quadratic nature
• C. linear nature
• D. sinusoidal nature

Answer 1

The correct option is C linear nature

$I\alpha =\tau \Rightarrow \alpha =\frac{\tau }{I}\omega =\alpha t=\frac{\tau t}{I}\rho =\frac{dKE}{dt}=\frac{d\left(\frac{1}{2}I{\omega }^2\right)}{dt}=\frac{d\left(\frac{1}{2}\frac{{\tau }^2{t}^2}{t}\right)}{dt}=\frac{{\tau }^2}{I}t$

Thus we see that $\rho \propto t$

Hence the power devlopedby the torque with respect to time is of linear nature.