A stone of mass 900g is tied to a string and moved in a vertical...

Given that 

Given the mass $m = 900g = \dfrac{900}{1000}kg = \dfrac{9}{10}kg$,

The radius of the circular path $r = 1m$

And, the angular velocity

$\omega = \dfrac{2\pi N}{60} = \dfrac{2\pi ( 10 )}{60} = \dfrac{\pi}{3}rad{s}^{- 1}$

With reference to the above diagram, the formula to calculate the tension at the lowermost point can be written as

$T - mg = mr{\omega}^{2} ⇒ T = mg + mr{\omega}^{2} . . . \left(1\right)$

From equation (1), it follows that

$\begin{cases}T & = & \dfrac{9}{10} \times 9 . 8 + \dfrac{9}{10} \times 1{\left(\dfrac{\pi}{3}\right)}^{2} \\ & = & 8 . 82 + \dfrac{9}{10} \times \dfrac{{\pi}^{2}}{9} \\ & = & 8 . 82 + 0 . 98 \\ & = & 9 . 8N\end{cases}$