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Question Number 31292 by ajfour last updated on 05/Mar/18

Commented by ajfour last updated on 05/Mar/18

$$LengthoftapeisL.$$

Commented by mrW2 last updated on 07/Mar/18

$$anysolutiongiven?$$

Commented by ajfour last updated on 07/Mar/18

$$Answergiven.$$

Answered by ajfour last updated on 07/Mar/18

Commented by ajfour last updated on 07/Mar/18

$$mgr\sin \theta =\left(\frac{3}{2}{mr}^2\right)\left(\frac{1}{r}\right)\left(\frac{vdv}{dx}\right)$$$$\Rightarrow {\int }_0^{v}vdv=\frac{2g\sin \theta }{3}{\int }_0^{x}dx$$$$\Rightarrow \frac{v^2}{2}=\frac{2gx\sin \theta }{3}$$$$\Rightarrow v=\sqrt{\frac{4g\sin \theta }{3}}\sqrt{x}$$$${\int }_0^L\frac{dx}{\sqrt{x}}=\sqrt{\frac{4g\sin \theta }{3}}{\int }_0^{t}dt$$$$2\sqrt{L}=\left(\sqrt{\frac{4g\sin \theta }{3}}\right)t$$$$ort=\sqrt{\frac{3L}{g\sin \theta }}.$$

Commented by rahul 19 last updated on 08/Mar/18

$$sir,why{I}_{cm}=\frac{3}{2}{mr}^2?$$$$assumingittobediscweget,$$$$\frac{{mr}^2}{4}+{mr}^2=\frac{5}{4}{mr}^2.butuhavetaken$$$$as\frac{{mr}^2}{2}+{mr}^2??(iamtakingtorque$$$$aboutthesurface).$$

Commented by mrW2 last updated on 08/Mar/18

$$forsoliddisc\frac{{mr}^2}{2}+{mr}^{2}iscorrectsir.$$

Commented by rahul 19 last updated on 08/Mar/18

$$whereamiwrong?{can}^{\prime }titake$$$$torquealongthesurface.(slant$$$$surfaceofwedge)?$$

Commented by mrW2 last updated on 08/Mar/18

$$I_0=\frac{{mr}^2}{2}forsoliddisc.$$

Commented by rahul 19 last updated on 08/Mar/18

$$yessir,itiswhenaxisisperpendicular$$$$todiscbutiamtakingalongsurface.$$

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