Question 642: Centre of Mass and Rotational Motion

Question

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of 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 (Esphere / Ecylinder) will be

Accepted Answer

$${{{E_{Sphere}}} \over {{E_{Cylinder}}}} = {{{1 \over 2}{I_s}\omega _s^2} \over {{1 \over 2}{I_c}\omega _c^2}} = {{{I_s}\omega _s^2} \over {{I_c}\omega _c^2}}$$
Here, $${I_s} = {2 \over 5}m{R^2}$$,   $${I_c} = {1 \over 2}m{R^2}$$
$${\omega _c} = 2{\omega _s}$$
$${{{E_{Sphere}}} \over {{E_{Cylinder}}}} = {{{2 \over 5}m{R^2} 	imes \omega _s^2} \over {{1 \over 2}m{R^2} 	imes {{\left( {2{\omega _2}} ight)}^2}}}$$
$$ \Rightarrow {4 \over 5} 	imes {1 \over 4} = {1 \over 5}$$

Answer

2 : 3

Answer

1 : 5

Answer

1 : 4

Answer

3 : 1

Centre of Mass and Rotational Motion

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of 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 (Esphere / Ecylinder) will be

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