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:

$A$ mass of $2 \, kg$ is suspended with a thread $AB$ as shown in the figure. $A$ thread $CD$ of the same type is attached to the other end of the $2 \, kg$ mass. The lower thread is pulled gradually,harder and harder in the downward direction,so as to apply force on $AB$. Which of the threads will break and why?

Two blocks of $7\,kg$ and $5\,kg$ are connected by a heavy rope of mass $4\,kg$. An upward force of $200\,N$ is applied as shown in the diagram. The tension at the top of the heavy rope at point $P$ is ....... $N$ $(g = 10\,m/s^2)$.

$A$ 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:

For the given system, what is the strain in wire $W_1$? Assume the wire $W_1$ connects the two blocks on the table, and wire $W_2$ connects the second block to the hanging mass.

On a smooth plane surface,two blocks $A$ and $B$ are accelerated by applying a force of $15 \, N$ on block $A$. If the mass of block $B$ is twice that of block $A$,the force on block $B$ is ........... $N$.