A light frictionless pulley is suspended with the help of a light spring. One end p of a light inextensible thread that passes over the pulley is free and the other end is tied to another light spring that is affixed to the ground at its Iower end as shown in the figure. Stiffness of both the springs is $k=500$ $\mathrm{N} {\mathrm{m}}^{-1}$. The free end $P$ is $h=10.0 \mathrm{cm}$ above the ground. The minimum pull at the end $P$ will bring is to the ground is $\frac{kh}{n}$, then find $\mathrm{n}$.

An inclined plane making an angle of $30°$ with the horizontal is placed in a uniform horizontal electric field $200\frac{\mathrm{N}}{\mathrm{C}}$ as shown in the figure. A body of mass $1 \mathrm{kg}$ and charge $5 \mathrm{mC}$ is allowed to slide down from rest at a height of $1 \mathrm{m}$. If the coefficient of friction is $0.2,$ find the time taken by the body to reach the bottom.
$\left[g=9.8 \mathrm{m} {\mathrm{s}}^{-2}; \sin 30°=\frac{1}{2}; \cos 30°=\frac{\sqrt{3}}{2}\right]$

A steel block of $10 \mathrm{kg}$ rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2 \mathrm{m} {\mathrm{s}}^{-2}.$ The normal reaction $R^{\text{'}}$ by the floor if mass of the iron cylinders are equal and of $20 \mathrm{kg}$ each is $\left(\text{in} \mathrm{N}\right)$,

[Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $\left.{\mu }_{\mathrm{s}}=0.2\right]$

An object of mass $m$ is being moved with a constant velocity under the action of an applied force of $2 \mathrm{N}$ along a frictionless surface with following surface profile.

The correct applied force vs distance graph will be :

A boy of mass $4 \mathrm{kg}$ is standing on a piece of wood having mass $5 \mathrm{kg}$. If the coefficient of friction between the wood and the floor is $0.5 ,$ the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _______ $\mathrm{N}$. (Round off to the Nearest Integer)

[Take $\left.g=10{ \mathrm{m} \mathrm{s}}^{-2}\right]$

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

The boxes of masses $2 \mathrm{kg}$ and $8 \mathrm{kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8 \mathrm{kg}$ to strike the ground starting from rest.  $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ 

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is:
Given $m=8 \mathrm{kg}, M=16 \mathrm{kg}$
Assume all the surfaces shown in the figure to be frictionless.

In the arrangement shown in figure $a_1,a_2,a_3$ and$a{ }_{4 }$  are the accelerations of masses $m_1,m_2,m_3$ and $m_4$ respectively. Which of the following relation is true for this arrangement?

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 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.

Two blocks $A$ and $B$ of masses $1.5 \mathrm{kg}$ and $0.5 \mathrm{kg}$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block A is lifted until block B touches the ground and then block A is released. The initial height of block A is $80 \mathrm{cm}$ when block B just touches the ground. The maximum height reached by block $\mathrm{B}$ from the ground after the block A falls on the ground is

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is $0.05.$ ($g=10 \mathrm{m} {\mathrm{s}}^{-2},$ mass of the string is negligible and no other friction exists).

The machine as shown has $2$ rods of length $1 \mathrm{m}$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a $2 \mathrm{kg}$ weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :