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
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Total kinetic energy of a rolling disc `=(1)/(2)mv^2 + (1)/(2)Iomega^2` `K.E = (3)/(4)mv^2` For surface AB `k.E_i+ loss in gravitational potential energy = K.E_f` `(3)/(4)m(3)^3 + mg(30) =(3)/(4) mV_B^2 …..(i)` For surface CD` `(3)/(4)m (v_2)^2 +mg(27) = (3)/(4)mV_D^2 ....(ii)` Given `V_B =B_D.` Therefore from (i) and (ii) `(3)/(4)m(3)^2+mgxx30 =(3)/(4)m(v_2)^2 + mgxx27` `:.v_2 =7`
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