Question

a disc starts from rest with an angular acceleration completes 10 revolutions in 2 seconds. the time taken by it to complete 10 more revolution from that instant is​

Answer 1

Starting from rest, the disc completes $\theta$ revolutions after $t$ seconds according to

$\theta=\dfrac\alpha2t^2$

with angular acceleration $\alpha$. It completes 10 rev in 2 s, which means

$10\,\mathrm{rev}=\dfrac\alpha2(2\,\mathrm s)^2\implies\alpha=5\dfrac{\rm rev}{\mathrm s^2}$

Find the time it takes to complete 20 rev with this acceleration:

$20\,\mathrm{rev}=\dfrac12\left(5\dfrac{\rm rev}{\mathrm s^2}\right)t^2\implies t=\sqrt8\,\mathrm s\approx2.83\,\mathrm s$

so it takes approximately 0.83 s to complete 10 more rev.