A rod is hinged at its centre and rotated by applying a constant torque starting from rest. The power developed by the external torque as a function of time is:
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Question

A rod is hinged at its centre and rotated by applying a constant torque starting from rest. The power developed by the external torque as a function of time is:

G1 Physics · Accepted Answer

Let the constant torque be τ. Since τ=Iα, α=τ/I is constant. Starting from rest, ω=αt=(τ/I)t. Instantaneous rotational power is P=τω. Therefore P=(τ²/I)t, so P is directly proportional to t. The P–t graph is a straight line through the origin, corresponding to Image 2. Hence option B.