The horizontal force applied on the wedge is:

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 :

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).

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

Three forces of magnitude $6 \mathrm{N}, 6 \mathrm{N}$ and $\sqrt{72} \mathrm{N}$ act at a cormer of a cube along three edges of a cube, as shown in the figure. The resultant of the three forces is

Two equal forces are acting at a point, making an angle of $60°$ with each other. If their resultant force is equal to $40\sqrt{3} \mathrm{N},$ the magnitude of each force is $\underline{ }$

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 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 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 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.

A rectangular frame of some mass has to be suspended symmetrically by two mass-less strings of equal length on two supports. It can be done in one of the three following ways as shown in below figures. The tension in the strings will be