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  • A thik spherical shell of radius lying on a rough horizontal surface is hit sharply and horizontally

A thik spherical shell of radius \mathrm{R} lying on a rough horizontal surface is hit sharply and horizontally by a cell.
 

Option: 1

\mathrm{\frac{3 R}{2}}

 


Option: 2

\mathrm{\frac{2 R}{3}}
 


Option: 3

\mathrm{\frac{R}{3}}
 


Option: 4

\mathrm{3R}


Answers (1)

best_answer

Apply conservation of angular momentum about the centre of the shall. If \mathrm{v} is the velocity of the centre of mass of the shell, then we can write-

\mathrm{L =I_{C m} \cdot \omega }

\mathrm{m v h =I_{C m} \cdot \omega}............(1)

but,\mathrm{ I_{C m}=\frac{2}{3} M R^2, \omega=\frac{V}{R} }

Equation (1) become -

\mathrm{\text { mvh } =\frac{2}{3} m R^2 \times \frac{V}{R} }.

\mathrm{h =\frac{2 R}{3} }

Hence option 2 is correct.



 

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