Three identical particles of mass $m$ are joined together by a thread as shown in the figure. All three particles are moving in a horizontal plane in a circle about the point $O$. If the velocity of the outermost particle is $v_0$,then the ratio of tensions in the three sections of the string is:

Two masses of $4\, kg$ and $5 \,kg$ are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of the $5\, kg$ mass is ........... $m/s^2$.

$A$ uniform thick string of length $5\,m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $5\,N$ from one end. The tension in the string at $1\,m$ from the force applied is ......... $N$.

An $80\, kg$ person is parachuting and is experiencing a downward acceleration of $2.8\, m/s^2$. The mass of the parachute is $5\, kg$. The upward force on the open parachute is ........... $N$ (Take $g = 9.8\, m/s^2$)

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface. The acceleration of mass $m$ is:

$A$ small block of mass $m$ is placed on a wedge of mass $M$ as shown,which is initially at rest. All the surfaces are frictionless. The spring attached to the other end of the wedge has a force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down,then the maximum retardation of $M$ is: