Question

A small cubical block of mass $1$ kg is placed inside a rough rectangular groove $\mu =12$ made in a circular table as shown in the figure. The table starts rotating with angular acceleration $1rad{s}^{-2}$ in a horizontal plane about its axis. The time $10\sqrt{K}sec$ after which the blocks will start motion with respect to the table. Find the value of $K$. (Take $g=10m/s^2$) Assume the size of block slightly smaller than the width of the groove.

Answer 1

Relative motion between block and table will start when,

$m{\omega }^{2}r\sin \theta =\mu (mg+m{\omega }^{2}r\cos \theta )$............(i)

$\omega =\alpha t$........(ii)

Solving (i) and (ii)

$t=\sqrt{\frac{10}{4}}$