A point $P(R\sqrt{3}, 0, 0)$ lies on the axis of a ring of mass M and radius R. The ring is located in y - z plane with its centre at origin O. A small particle of mass m starts from P and reaches O under gravitational attraction only. Its speed at O will be.

$\sqrt{\frac{G M}{R}}$

$\left(\begin{array}{c}\text { Total } \\ \text { Mechanical } \\ \text { Energy }\end{array}\right)_{\mathrm{P}}=\left(\begin{array}{c}\text { Total } \\ \text { Mechanical } \\ \text { Energy }\end{array}\right)_{\mathrm{O}}$

$\Rightarrow \frac{1}{2} \mathrm{~m}(0)^2-\frac{\mathrm{GMm}}{\sqrt{(\sqrt{3} \mathrm{R})^2+\mathrm{R}^2}}=\frac{1}{2} \mathrm{mv}^2-\frac{\mathrm{GMm}}{\mathrm{R}}$

$\Rightarrow-\frac{\mathrm{GMm}}{2 \mathrm{R}}=\frac{1}{2} \mathrm{mv}^2-\frac{\mathrm{GMm}}{\mathrm{R}}$

$\Rightarrow \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$