$A$ particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30^\circ$ and $60^\circ$ from the vertical (lowest position) are $T_1$ and $T_2$ respectively. Then:

$A$ steel wire can withstand a load up to $2940 \ N$. $A$ load of $150 \ kg$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position,so that the wire does not break when the load passes through the position of equilibrium,is (in $^{\circ}$)

$A$ 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 $g = 10 \,m/s^2$)

If a particle completes a vertical circular motion,what is the ratio of its velocities at points $A$,$B$,and $C$?

$A$ block of mass $m$ is given a velocity $20\ m/s$ on a horizontal rough surface of length $x\ m$. After the rough surface,there is a vertical circular path of radius $R = 2\ m$ which is frictionless. The block enters the circular path with the minimum velocity required to complete the path. Find the length of the rough surface $x$ if the coefficient of friction is $\mu = 0.5$.

$A$ point mass '$m$' attached at one end of a massless,inextensible string of length '$\ell$' performs a vertical circular motion and the string rotates in a vertical plane,as shown in the diagram. The increase in the centripetal acceleration of the point mass when it moves from point $A$ to point $C$ is $(g = \text{acceleration due to gravity})$: