A sphere of radius 209 cm and a spherical shell of radius 69

A sphere of radius 2.09 cm and a spherical shell of radius 6.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the sphere\\\'s angular speed to the spherical shell\\\'s angular speed be?

Solution

Here ,

let the mass of each is m

r1 = 2.09 cm

r2 = 6.97 cm

let the angular speed of sphere is w1

angular speed of spherical shell is w2

as the kinetic energy of both is equal

0.5 * 0.4 * m * 2.09^2 * w1^2 = 0.5 * (2/3 m * 6.97^2) * w2^2

w1/w2 = 4.305

the ratio of the sphere\'s angular speed to the spherical shell\'s angular speed be 4.305