Ten one-rupee coins are placed on top of each other on a table. Each coin has mass $m$. The reaction force of the $6^{th}$ coin (counted from the bottom) on the $7^{th}$ coin is .......... $mg$.

Two particles each of mass $m$ are moving in horizontal circles with the same angular speed $\omega$. If both strings are of the same length $l$,find the ratio of tension in the strings $\frac{T_1}{T_2}$.

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:

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If the surface between $M$ and $m_0$ has a coefficient of friction $\mu$,find the tension in the string,assuming the system moves together.

Three blocks of masses $4 \ kg$, $2 \ kg$, and $1 \ kg$ respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \ N$ is applied on the $4 \ kg$ block, the contact force between the $4 \ kg$ and the $2 \ kg$ block will be: (in $N$)

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 ....... $N$ $(g = 10\,m/s^2)$.