At time t = 0 , a horizontal disc starts rotating with angular acceleration 1 rad s - 2 ⁡ about an axis perpendicular to its plane and passing through its Centre. A small block is lying on this disc a

Question

At time t = 0 , a horizontal disc starts rotating with angular acceleration 1 rad s - 2 ⁡ about an axis perpendicular to its plane and passing through its Centre. A small block is lying on this disc at a distance 0 . 5 m from the centre, coefficient of friction between the surface of block and disc is 0 . 255 . The block will start slipping on the disc at time t , which is approximately equal to

TestHub · Accepted Answer

The block will start slipping on the table when friction will reach its limiting value.

$f = m \sqrt{{(α r)}^{2} + {(α t)}^{4} r^{2}} = μ m g$

$m \sqrt{{(α r)}^{2} + {(α t)}^{4} r^{2}} = μ m g$

$\Rightarrow α^{2} r^{2} + α^{4} r^{2} t^{4} = μ^{2} g^{2}$

$\Rightarrow t = {(\frac{μ^{2} g^{2} - α^{2} r^{2}}{α^{4} r^{2}})}^{1 / 4}$

$\Rightarrow t = \sqrt{5} s$

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