A system of $10$ balls each of mass $2 \mathrm{kg}$ are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7^{\mathrm{th} }$ and $8^{\mathrm{th} }$ ball is _____  $\mathrm{N}$ when $6^{\mathrm{th} }$ ball just leaves the table.

A system of two blocks of masses $m=2 \mathrm{kg}$ and $M=8 \mathrm{kg}$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A mass of $10 \mathrm{kg}$ is suspended vertically by a rope of length $5 \mathrm{m}$ from the roof. A force of $30 \mathrm{N}$ is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\alpha ={\tan }^{-1}\left(x\times {10}^{-1}\right)$. The value of $x$ is _____ .

(Given, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A hanging mass $M$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $2\mathrm{Mg}$ force. In this situation, tension in the string is $\frac{x}{5}\mathrm{Mg}$ for $x=$_____. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
(Given $g=$ acceleration due to gravity)

A uniform disc with mass $M=4 \mathrm{kg}$ and radius $R=10 \mathrm{cm}$ is mounted on a fixed horizontal axle as shown in figure. A block with mass $m=2 \mathrm{kg}$ hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ $\mathrm{N}$.

(Take $g=10{ \mathrm{m} \mathrm{s}}^{-2}$)

A block of metal weighing $2 \mathrm{kg}$ is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \mathrm{kg} {\mathrm{s}}^{-1}$ and at a speed of $10{ \mathrm{m} \mathrm{s}}^{-1}$. Then, the initial acceleration of the block, in $\mathrm{m} {\mathrm{s}}^{-2}$, will be

A block of mass $40 \mathrm{kg}$ slides over a surface, when a mass of $4 \mathrm{kg}$ is suspended through an inextensible massless string passing over frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is $0.02$. The acceleration of block is: (Given $g=10{ \mathrm{m} \mathrm{s}}^{-2}$.)