Equilibrium, Third Law & Frames

Which of the following person is in an inertial frame of reference?

A flexible chain of mass $m$ hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $30^\circ$. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is ______.

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $T_1$ and $T_2$, respectively, are (in N):

(Take acceleration due to gravity $10\text{ m/s}^2$)

Which one of the following person is in an inertial frame of reference?

A mass ' M ' is suspended by a rope from a rigid support at point ' P ' as shown in figure. Another rope is tied at end ' Q ' and pulled horizontally with a force ' $F$ '. If the rope makes an angle ' $\theta$ ' with vertical then the tension in the string ' PQ ' is

A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1 = \sqrt{3}T_2$, the angles $\theta_1$ and $\theta_2$ are

A body of weight $200\text{ N}$ is suspended from a tree branch through a chain of mass $10\text{ kg}$. The branch pulls the chain by a force equal to (if $g = 10\text{ m/s}^2$):

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

A $1\text{ kg}$ mass is suspended from the ceiling by a rope of length $4\text{ m}$. A horizontal force '$F$' is applied at the mid point of the rope so that the rope makes an angle of $45^\circ$ with respect to the vertical axis as shown in figure. The magnitude of $F$ is:

(Assume that the system is in equilibrium and $g = 10\text{ m/s}^2$)

Three forces $F_1 = 10\text{ N},\ F_2 = 8\text{ N},\ F_3 = 6\text{ N}$ are acting on a particle of mass $5\text{ kg}$. The forces $F_2$ and $F_3$ are applied perpendicularly so that particle remains at rest. If the force $F_1$ is removed, then the acceleration of the particle is:

A block of $\sqrt{3}\text{ kg}$ is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30^\circ$ with the wall. The tension $T$ is: (Given $g = 10\text{ m s}^{-2}$)

A door $1.2\text{ m}$ wide requires a force of $1\text{ N}$ to be applied perpendicular at the free end to open or close it. The perpendicular force required at a point $0.2\text{ m}$ distant from the hinges for opening or closing the door is

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is $1 : x$ where $x =$ _____________.

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

(Given, g = 10 m/s2)

Statement: 1

If three forces $\vec{F}_1, \vec{F}_2$ and $\vec{F}_3$ are represented by three sides of a triangle and $\vec{F}_1 + \vec{F}_2 = -\vec{F}_3$, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement: 2

A triangle made up of three forces $\vec{F}_1, \vec{F}_2$ and $\vec{F}_3$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.

In the light of the above statements, choose the most appropriate answer from the options given below:

A car is moving on a plane inclined at 30$^\circ$ to the horizontal with an acceleration of 10 ms${}^{-2}$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ______________. (Take g = 10 ms${}^{-2}$)

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45° with the vertical. Then F equal: (Take g = 10 ms–2 and the rope to be massless)

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviates at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms${}^{-2}$)

A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of $a$. The pendulum will tilt

A uniform sphere of weight W and radius 5 cm is being held by a string as shown in the figure. The tension in the string will be:

Three forces acting on a body are shown in the figure. To have the resultant force only along the y- direction, the magnitude of the minimum additional force needed is

Three forces start acting simultaneously on a particle moving with velocity,$\vec{v}$ These forces are represented in magnitude and direction by the three sides of a triangle $ABC$. The particle will now move with velocity

When forces $F_1,\ F_2,\ F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the acceleration of the particle is

Two forces are such that the sum of their magnitudes is $18\text{ N}$ and their resultant is $12\text{ N}$ which is perpendicular to the smaller force. Then the magnitudes of the forces are