A weightless thread can support tension upto $30 \,N$. A stone of mass $0.5 \,kg$ is tied to it and is revolved in a circular path of radius $2 \,m$ in a vertical plane. If $g = 10m/{s^2}$, then the maximum angular velocity of the stone will be ........ $rad/s$
A weightless thread can support tension upto $30 \,N$. A stone of mass $0.5 \,kg$ is tied to it and is revolved in a circular path of radius $2 \,m$ in a vertical plane. If $g = 10m/{s^2}$, then the maximum angular velocity of the stone will be ........ $rad/s$
$5$
$\sqrt {30}$
$\sqrt {60}$
$10$
A weightless thread can support tension upto $30 \,N$. A stone of mass $0.5 \,kg$ is tied to it and is revolved in a circular path of radius $2 \,m$ in a vertical plane. If $g = 10m/{s^2}$, then the maximum angular velocity of the stone will be ........ $rad/s$
${T_{\max }} = m\omega _{^{\max }}^2r + mg$
$⇒$ $\frac{{{T_{\max }}}}{m} = {\omega ^2}r + g$
$⇒$ $\frac{{30}}{{0.5}} - 10 = {\omega ^2}_{\max }r$
$⇒$ ${\omega _{\max }} = \sqrt {\frac{{50}}{r}} = \sqrt {\frac{{50}}{2}} = 5\,rad/s$