$A$ smooth inclined plane ends in a vertical circular loop,as shown in the figure. $A$ small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of the circle,then the height $h = \alpha R$. The value of $\alpha$ is . . . . . . .

$A$ particle of mass $200 \,g$ is moving in a circle of radius $2 \,m$. The particle is just 'looping the loop'. What are the speed of the particle and the tension in the string at the highest point of the circular path? (Take $g = 10 \,m/s^2$)

$A$ $2 \, kg$ 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 $70 \, N$? $(g = 10 \, m/s^2)$.

$A$ particle of mass $m$ is tied to one end of a string of length $l$. The particle is held horizontal with the string taut. It is then projected upward with a velocity $u$. The tension in the string is $\frac{mg}{2}$ when it is inclined at an angle $30^o$ to the horizontal. The value of $u$ is

$A$ particle starts sliding from the top of a sphere of diameter $42 \, m$. At what height from the bottom of the sphere will the particle lose contact with the sphere?

$A$ stone of mass $150 \ g$ moves in a vertical circle at the end of a string. The radius of the circle is $70 \ cm$ and the speed of the stone at the topmost point $P$ is $3.5 \ m/s$. For the instant at which the stone passes through the highest point $P$,the centripetal force is nearly ......... $N$ (take $g = 10 \ m/s^2$).