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  • Consider a solid cylindre of uniform mass density and very thin cylindrical shell of uniform mass per unit area. They have the same radius and total mass. If they are both rolling on a plane withou

Consider a solid cylindre of uniform mass density and very thin cylindrical shell of uniform mass per unit area. They have the same radius and total mass. If they are both rolling on a plane without slipping with the same angular velocity, the ratio of the Kinetic energies of the solid cylinder to that of the shell is -
 

Option: 1

3:4


Option: 2

1:2


Option: 3

1:1


Option: 4

2:1


Answers (1)

best_answer

Case -I

\mathrm{(k \cdot E \cdot)_{\text {sphere }}=\frac{1}{2} m v^2\left(1+\frac{k^2}{R^2}\right)}

                                  \mathrm{=\frac{1}{2}mv^{2}\left ( 1+\frac{1}{2} \right )}                              \mathrm{\because \frac{k^{2}}{R^{2}}=\frac{1}{2}}


\mathrm{(k-E)_S =\frac{1}{2} m v^2 \times \frac{3}{2} }

                  \mathrm{ =\frac{3}{4} m v^2 }                      

Case II -

\mathrm{(k \cdot E \cdot)_{\text {Hollow }} =\frac{1}{2} m v^2[1+1] }

                                    

    \mathrm{ =m v^2} \\ {\quad\quad\quad \because \frac{k^2}{R^2}=1}

\mathrm{ \therefore \quad \frac{k \cdot E _{s}}{k \cdot E_H}=\frac{3}{4} }

Hence option 1 is correct.





 

 

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manish

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