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Question Number 31187 by rahul 19 last updated on 03/Mar/18

Commented by ajfour last updated on 03/Mar/18

Commented by ajfour last updated on 03/Mar/18

$$v=\omega (R+r)$$$$u=\omega R$$$$\Rightarrow \mathit{u}=\frac{\mathit{v}\mathit{R}}{\mathit{R}+\mathit{r}}$$$$displacementofpointAbythetime$$$$spoolmakesonerotation$$$$s_A=vT=v\left(\frac{2\pi }{\omega }\right)=v\times \frac{2\pi }{\left(\frac{v}{R+r}\right)}$$$$=2\mathit{\pi }(\mathit{R}+\mathit{r})$$$$x=utandx=R\cot \left(\frac{\theta }{2}\right)$$$$\Rightarrow R\cot \left(\frac{\theta }{2}\right)=ut$$$$\Rightarrow -\frac{R}{2}\mathrm{cosec}{}^2\left(\theta /2\right)\frac{d\theta }{dt}=u=\frac{vR}{R+r}$$$$\Rightarrow \mid \frac{d\theta }{dt}\mid =\left(\frac{2\mathit{v}}{\mathit{R}+\mathit{r}}\right)\sin {}^2\left(\frac{\alpha }{2}\right)$$$$hence\left(3\right),and\left(4\right)arecorrect.$$

Commented by rahul 19 last updated on 03/Mar/18

$$butcorrectans.isACD.$$

Commented by ajfour last updated on 03/Mar/18

$$\left(A\right){isn}^{\prime }tcorrect.$$

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