Question

Two small wooden blocks are placed on a circular rotating table of radius 1 m at distance 10 cm and 60 cm from the centre of the table. The table is rotating with angular velocity 4 rad s^-1 about its axis of rotation. Out of these two blocks which one continues to revolve with the table. Given μ = 0.2

Answer 1

r = 1 m, ω = 4 rad s^-1, μ = 0.2

The wooden block will continue to revolve with table if force of friction is equal to or greater than the centripetal force required by it.

i.e., F ≥ {mv²}/{r}

Since F = μR = μ mg

Hence μ mg = mv²/r or, μ mg ≥ mr ω²  (∴ v = ωr)

or mrω² = μ mg or, r ≤ μg/ω²

or, r ≤ {0.2 x 9.8}/{16} ≤ 0.123 m

Thus, the block placed at 100 cm will revolve with the table.