A particle is moving in the vertical plane. It is attached at one end of a string of length $l$ whose other end is fixed. The velocity at the lowest point is $u$. The tension in the string $\overrightarrow{T}$ is and acceleration of the particle $\overrightarrow{a}$ is at any position. Then, $\overrightarrow{T}.\overrightarrow{a}$ is zero at the highest point

A particle is moving in the vertical plane. It is attached at one end of a string of length I whose other end is fixed. The velocity at the lowest point is $u$. The tension in the string $\overrightarrow{T}$ is and acceleration of the particle $\overrightarrow{a}$ is at any position. Then, $\overrightarrow{T}.\overrightarrow{a}$ is zero at the highest point.

In the above question, $\overrightarrow{T}.\overrightarrow{a}$ is non-negative at the lowest point for 

A particle is moving in a circular path on the vertical plane. It is attached at one end of a string of length I whose other end is fixed. The velocity of the particle at the lowest point is $u$. The tension in the string is $\overrightarrow{T}$ and the acceleration of the particle is $\overrightarrow{a}$ at any position. Then, $\overrightarrow{T}.\overrightarrow{a}$ is zero at the highest point if

A bob of mass $M$ is suspended by a massless string of length $L$. The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies