$A$ stone of mass $1 \,kg$ is tied with a string and it is whirled in a vertical circle of radius $1 \,m$. If tension at the highest point is $14 \,N$,then velocity at the lowest point will be ............ $m/s$.

What will be the minimum speed of the roller-coaster so that the passenger at the top, when becomes upside down, does not fall out (in $m \ s^{-1}$)? Consider the acceleration due to gravity as $10 \ m \ s^{-2}$, and the radius of curvature of the roller coaster is $10 \ m$.

$A$ $2 \, kg$ mass is attached to a string of length $1 \, m$ and is whirled in a vertical circle at a constant speed of $5 \, m/s$. At what position will the tension in the string be $70 \, N$? $(g = 10 \, m/s^2)$.

$A$ pendulum consisting of a small sphere of mass $m$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2mg$,then the maximum angular amplitude of the displacement from the vertical can be ....... $^o$

$A$ body of mass $0.4\, kg$ is whirled in a vertical circle making $2\, rev/sec$. If the radius of the circle is $2\, m$,then tension in the string when the body is at the top of the circle,is ......... $N$.

$A$ weightless thread can support a tension of up to $30 \, N$. $A$ 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 $g = 10 \, m/s^2$,then the maximum angular velocity of the stone will be ........ $rad/s$.