Q130 / 160 · AP EAMCET 2023 (15 May Shift 2) · Physics

The angular peed of a rigid body rotating about a fixed axis is $(8-2 t) \mathrm{rad} \mathrm{s}^{-1}$. The angle through which the body rotates before it comes to rest is

  • A
    $8 \mathrm{rad}$
  • B
    $12 \mathrm{rad}$
  • Correct answer
    C
    $16 \mathrm{rad}$
  • D
    $20 \mathrm{rad}$

Solution

Angular speed, $\omega=8-2 \mathrm{trad} / \mathrm{s}$ $\begin{aligned} & \frac{\mathrm{d} \theta}{\mathrm{dt}}=8-2 \mathrm{t} \\ & \Rightarrow \int_{\mathrm{d} \theta}=\int(8-2 \mathrm{t}) \mathrm{dt} \\ & \theta=8 \mathrm{t}-\frac{2 \mathrm{t}^2}{2}=8 \mathrm{t}-\mathrm{t}^2 \\ & \text { When } \omega=0 \\ & 8-2 \mathrm{t}=0 \Rightarrow \mathrm{t}=4 \mathrm{~s} \\ & \theta=8 \times 4-4^2=32-16 \\ & \theta=16 \mathrm{rad} \end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions