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A spherical shell of radius 4.34 cm and a sphere of radius 6.72 cm are rolling w

ID: 1910228 • Letter: A

Question

A spherical shell of radius 4.34 cm and a sphere of radius 6.72 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 spherical shell's angular speed to the sphere's angular speed be?

Explanation / Answer

We generally do not answer the questions of those who are having low rating. You are having a rating of "95%". Please rate all answers and improve your rating. Even if you find the answers are incorrect, first rate Lifesaver or helpful to the best answer and then rate other answers as not helpful. But do rate them for the good of both of us. Thanks!! Coming to the problem Let subscript 1 denotes spherical shell and subscript 2 denotes sphere. They have the same total kinetic energy =>0.5*m1*v1^2 + 0.5*I1*w1^2 = 0.5*m2*v2^2 + 0.5*I2*w2^2 =>0.5*m1*r1^2*w1^2 + 0.5*I1*w1^2 = 0.5*m2*r2^2*w2^2 + 0.5*I2*w2^2 =>w1^2*(0.5*m1*r1^2+ 0.5*I1) = w2^2*(0.5*m2*r2^2+0.5*I2) =>w1^2/w2^2 = (0.5*m2*r2^2+0.5*I2)/(0.5*m1*r1^2+ 0.5*I1) I1 = (2/3)*(4.34^2)*m, I2 = (2/5)*(6.72^2)*m r1 = 4.34, r2 = 6.72 =>w1^2/w2^2 = ((0.5*(6.72^2))+(0.5*(2/5)*(6.72^2)))/((0.5*(4.34^2))+(0.5*(2/3)*(4.34^2))) = 2.014 =>w1/w2 = 1.419

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