A disc of mass M and radius R has a spring of constant k attached to its centre, the other end of the spring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the right does the centre of mass move, if initially the spring was unstretched and the angular speed of the disc was ω 0

Question

A disc of mass M and radius R has a spring of constant k attached to its centre, the other end of the spring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the right does the centre of mass move, if initially the spring was unstretched and the angular speed of the disc was ω 0, R ω 2 M / 3 k, R ω 3 M / 2 k, R ω M / k, R ω M / 2 k

MARKS App · Accepted Answer

Due to pure rolling E t = 0 = E t = 1 I = MR 2 2 V cm = ω R E t = 0 = 1 2 MV cm 2 + 1 2 I cm ω 2 1 2 M ω 2 R 2 + 1 2 MR 2 2 × ω 2 1 2 × 3 2 M ω 2 R 2 E t = T = 1 2 kx 2 1 2 × 3 2 M ω 2 R 2 = 1 2 kx 2 x = ω R 3 M 2 k

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