Question

A small wedge whose base is horizontal is fixed to a vertical rod as shown in Fig. The sloping side of the wedge is frictionless and the wedge is spun with a constant angular speed $\omega$ about vertical axis as shown in the figure. Find the
a. value of angular speed $\omega$ for which the block of mass m just does not slide down the wedge.
b. normal reaction on the block by wedge when block does not slip relative to wedge.

Answer 1

R.E.F image

Along x-axis

$\therefore$ block does not slide

$\therefore mg\sin \theta =mv{w}^{2}cos\theta$

$\therefore w=\sqrt{\frac{g}{r}tan\theta }$

Along y-axis

$N-mgcos\theta -mr{w}^{2}sin\theta =0$

$\therefore$ Normal reaction (N) $=mgcos\theta -mv{w}^{2}sin\theta$