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Two identical uniform discs roll without...

Two identical uniform discs roll without slipping on tow different sufaces AB and CD (see figure) starting at A and C with linear speeds `v_1 and v_2` respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed `v_1= 3m/s` then `v_2 in m/s` is (g = 10 m//s^2)`

Text Solution

Verified by Experts

Kinetic energy of a purely rolling disc `=1/2 mV^(2) + 1/2(m/2)v^(2) = 3/4 mV^(2)`
Using conservation of energy on both discs and equating their final energies.
`3/4 mV_(1)^(2) + mg.30 = 3/4 mV_(2)^(2) + mg. 27, 3mg = 3/4m(V_(2)^(2) -V_(1)^(2))`
`4g = V_(2)^(2) -9, V_(2)^(2) =49, V_(2)=7`.
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