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  • Shown in the figure is a hollow ice cream cone (it is open at the top). If its mass is 'M', radius of its top, R and height H, then its M.O.I about its axis is : <img alt="" src="https://cdn.entrance360.com/media/uploads/2020/09/06/wh

Shown in the figure is a hollow ice cream cone (it is open at the top). If its mass is 'M', radius of its top, R and height H, then its M.O.I about its axis is :


Option: 1 MH2/3
Option: 2 MR2/3
Option: 3 M(R2+H2)/4
Option: 4 MR2/3

Answers (1)

best_answer

We will take an elemental ring of thickness dy and radius r at a slant height y as show in the figure

\begin{array}{l}\\ given, \ \operatorname{Mass}=M \\ \operatorname{Radius}=R \\ I_{H C}=\int d I \operatorname{ring}=\int(d m) r^{2} \\ \\ d m=\frac{M}{\pi R \l}(2 \pi r d y) \end{array}

where dm is the mass of the elemental ring

I_{H C}= \int \frac{2 M}{R \ell} r^{3} d y

\frac{r}{R}=\frac{y}{l} \quad \Rightarrow \quad r=\frac{R}{l}y

I_{H C}=\frac{2 M}{Rl} \frac{R^{3}}{l^{3}} \int_{0}^{l} y^{3} d y=\frac{MR^2}{2}

Posted by

Deependra Verma

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