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  • A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation \left( {{{E_{{\rm sphere}} } \mathord{\left/ {\vphantom {{E_{{\rm sphere}} } {E_{{\rm cylinder}} }}} \right. \kern-\nulldelimiterspace} {E_{{\rm cylinder}} }}} \right) will be

Option: 1

2 : 3


Option: 2

1 : 5


Option: 3

1 : 4


Option: 4

3 : 1


Answers (1)

best_answer

Moment of inertia for solid sphere about diameter

I=\frac{2}{5} MR^{2}

Moment of inertia for solid cylinder About axis passing through central line.

I=\frac{1}{2} MR^{2}

Kinetic energy of rotation

K=\frac{1}{2}Iw^{2}

\\\frac{K_s}{K_c}=\frac{I_s}{I_C}(\frac{\omega_s^2}{\omega_c^2})=\frac{1}{5}

 

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chirag

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