Equilibrium of Forces

A block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

Two cubes of masses  $m_1$ and  $m_2$ be on two frictionless slopes of block A which rests on a horizontal table. The cubes are connected by a string which passes over a pulley as shown in the figure. To what horizontal acceleration f should the whole system (that is the blocks and cubes) be subjected so that the cubes do not slide down the planes? What is the tension of the string in this situation?

If resultant of these three forces is along $Y$-axis, then $F_3$ is equal to:

A force of $120 \mathrm{N}$ and a force of $20 \mathrm{N}$ acting simultaneously at a point may produce a resultant force of

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be :-

If a charge $q$ is placed at the centre of the line joining two equal charges $Q$ each such that the entire system is in equilibrium, then the value of $q$ is:

The force with which a man of mass. $60 \mathrm{kg}$ has to pull the rope to hold the plank at rest is (neglect the masses of plank, rope and pull) $\left(\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2\right)$

Two wooden blocks are moving on a smooth horizontal surface such that the mass $m$ remains stationary with respect to block of mass $M$ as shown in the figure. The magnitude of force $P$ is,

The mass $m$ moves in a circular arc of angular amplitude $60°$. The minimum coefficient of friction between $4m$ and surface of table to prevent slipping is,

A man of mass $50 \mathrm{kg}$ stands on a frame of mass $30 \mathrm{kg}$. He pulls on a light rope which passes over a pulley. The other end of the rope is attached to the frame. For the system to be in equilibrium what force man must exert on the rope?

Figure shows a man of mass $50 \mathrm{kg}$ standing on a light weighing machine kept in a box of mass $30 \mathrm{kg}.$ The box is hanging from a pulley fixed to the ceiling through a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, the weight shown by the machine is :

An iron sphere weighing $10 \mathrm{N}$ rests in a $V$ shaped smooth trough whose side form an angle of $60°$ as shown in the figure. Then reaction forces are

For next two question please follow the same

The system is released from rest with both the spring in unstretched positions. Mass of each block is 1 kg and force constant of each spring is 10 N/m.

Extension of horizontal spring in equilibrium is

A body of mass$\mathrm{m}$ is released from a height $\mathrm{h}$ on a smooth inclined plane that is shown in the figure. Which of the following can be true about the velocity of the block if it is known that the wedge is fixed ?

Three forces are acting on a body in equilibrium at the same time. Two of them are given as ${\overrightarrow{\mathrm{F}}}_1=2\hat{\mathrm{i}}-5\hat{\mathrm{j}}\text{,} {\overrightarrow{\mathrm{F}}}_2=3\hat{\mathrm{i}}-4\hat{\mathrm{j}}$. Find the third force ${\overrightarrow{\mathrm{F}}}_3$.

Three force $1 \mathrm{N}$ , $2 \mathrm{N}$ and $3 \mathrm{N}$ acting along different directions on a body in the same plane and at the same time.

Three forces are applied on a body and body is in eqilibrium .It is infered about sum of any two forces together that it

In the figure shown below, the tension in the string is

In an arrangement the bob of mass $2 \mathrm{kg}$ of a simple pendulum has a charge of $5.0 \mu \mathrm{C}$. A horizontal electric field of $2000 \mathrm{V}/\mathrm{m}$ exist in the region in which the bob remains at rest. The angle between string and vertical in equilibrium is,

A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statements is/are correct?



a. $\overrightarrow{N}+\overrightarrow{T}+\overrightarrow{W}=0$

b. $T^2=N^2+W^2$

c. $T=N+W$

d. $N=W\tan \theta$