In case of vertical circular motion of a particle by a thread of length \( r \), if the tension in the thread is zero at an angle \(30^\circ\) as shown in the figure, the velocity at the bottom point (A) of the vertical circular path is ( \( g \) = gravitational acceleration ). 
Find speed given to particle at lowest point so that tension in string at point A becomes zero. 


Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 