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O 4/5/2018 06:00 PM O 70.2/100 O 4/5/2018 04:52 PM -Print Calculator l Periodic Table Gradebook Question 7 of 7 IncorrectIncorrect IncorrectIncorrect Map Sapling Learning A sphere of radius 3.84 cm and a spherical shell of radius 7.72 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 sphere's angular speed to the spherical shell's angular speed be? Number sph shl Tools × 10 Previous Give Up & View Solution Check Answer Next Exit HintExplanation / Answer
Given That
r1 = 3.84cm
r2 = 7.72cm
M.I1 = 2/3m*r1^2
M.I2 = 2/5m*r2^2
KE = 1/2mv^2+1/2(M.I)^2*w^2
for rolling body
v = w*r
KE = 1/2m*w^2*r^2+1/2(M.I)^2*w^2
KE are same
=> w1^2(1/2m*r1^2+1/2*(2/3m*r1^2)) = W2^2(1/2m*r2^2+1/2*(2/5m*r2^2))
=> (w1/w2)^2 = (7/10*r2^2)/(5/6*r1^2)
=> (w1/w2)^2 = 42/50(r2/r1)^2
=> w1/w2 = (r2/r1)*Sqrt(42/50)
=> w1/w2 = (7.72/3.84)*0.9165
=> W1/W2 = 2.0104*0.9165
=> w1/w2 = 1.8
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