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  4. A uniform, thin cylindrical shell and solid cylinder roll horizontally without slipping. The speed of the cylindrical shell is v . The solid cylinder and the hollow cylinder encounter an incline that they climb without slipping. If the maximum height they reach is the same, find the initial speed v' of the solid cylinder.

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Q. A uniform, thin cylindrical shell and solid cylinder roll horizontally without slipping. The speed of the cylindrical shell is $v$ . The solid cylinder and the hollow cylinder encounter an incline that they climb without slipping. If the maximum height they reach is the same, find the initial speed $v'$ of the solid cylinder.

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

$KE=\frac{1}{2}m v^{2}+\frac{1}{2}I\omega ^{2}$
$\frac{3}{4}m v_{1}^{2}=m v_{2}^{2}$
$\frac{v_{1}}{v_{2}}=\sqrt{\frac{4}{3}}$