A uniform disc of mass m and radius R is projected on a rough horizontal floor with speed v₀ and no initial rotation. It starts pure rolling at time t₀. Which option gives the correct complete result for (i) centre speed at t₀, (ii) t₀, and (iii) work done by friction?

Question

G1 Physics · Accepted Answer

During sliding, friction f=µmg gives dv/dt=-µg and α=fR/I=2µg/R for a disc. Pure rolling begins when v=ωR, giving t₀=v₀/(3µg) and v(t₀)=2v₀/3. Work done by friction follows W=∫f·contact-point velocity dt, yielding W=½[3µ²mg²t²-2µmgtv₀] for t<t₀ and total W=-mv₀²/6 after rolling starts. Hence option A.