This post presents Numerical problems on Equilibrium. This physics worksheet will help students who are preparing for AP Physics, IIT JEE, and other competitive examinations to test their preparedness. This numerical set contains medium to hard problems from the equilibrium chapter.

**Numerical Problems on Equilibrium**

1 ) A 50 kg uniform square sign, 2.0 m on a side, is hung from a 3.0 m rod of negligible mass. A cable is attached to the end of the rod and to a point on the wall 4.0 m above the point where the rod is fixed to the wall, as shown below. (a) Calculate the tension in the cable. (b) Calculate the horizontal and vertical components of the force exerted by the wall on the rod.

2 ) Forces F_{1}, F_{2}, and F_{3} act on the structure below as shown. We wish to put the structure in equilibrium by applying a force, at a point such as P, whose vector components are F_{h} and F_{v}. We are given that a = 2.0 m, b = 3.0 m, c = 1.0 m, F_{1} = 20 N, F_{2} = 10 N, and F_{3} = 5.0 N. Calculate (a) F_{h}, (b) F_{v}, and (c) d.

3 ) One end of a uniform beam weighing 50 N and 3.0 m long is attached to a wall with a hinge. The other end is supported by a wire, as shown below. (a) Calculate the tension in the wire. (b) Calculate the horizontal and vertical components of the force of the hinge.

4 ) A nonuniform bar of weight W is suspended at rest in a horizontal position by two light cords as shown below. The angle one cord makes with the vertical is θ = 36.9 degree; the other makes the angle φ = 53.1 degree with the vertical. If the length L of the bar is 6.1 m, compute the distance x from the left-hand end to the center of gravity.

5 ) In the figure below, the length of the bar is 3.0 m and its weight is 200 N. Also, W = 300 N and θ = 30 degree. The wire can withstand a maximum tension of 500 N. (a) Calculate the maximum distance x possible before the wire breaks. (b) With W placed at this maximum x, calculate the horizontal and vertical components of the force exerted on the bar by the pin.

6 ) A 100 lb. plank, of length L = 20 ft, rests on the ground and on a frictionless roller at the top of a wall of height h = 10 ft. The center of gravity of the plank is at its center. The plank remains in equilibrium for any value of θ>= 70 degrees but slips if θ < 70 degrees. Find the coefficient of static friction between the plank and the ground.

7 ) A rope, assumed massless, is stretched horizontally between two supports that are 3.44 m apart. When an object of weight 3160 N is hung at the center of the rope, the rope is observed to sag by 35 cm. Calculate the tension in the rope.

8 ) The system below is in equilibrium, but it begins to slip if any additional mass is added to the 5.0 kg object. Calculate the coefficient of static friction between the 10 kg block and the plane on which it rests.

9 ) An automobile (mass = 1360 kg) has a wheelbase of 305 cm. Its center of gravity is located 178 cm behind the front axle. Determine (a) the force exerted on each of the front wheels (assumed the same) and (b) the force exerted on each of the back wheels (assumed the same) by the level ground.

10 ) A diver of weight 580 N stands at the end of a 4.5 m diving board of negligible weight. The board is attached by two pedestals 1.5 m apart, as shown below. Find the tension (or compression) in each of the two pedestals.

11 ) The system below is in equilibrium with the string in the center exactly horizontal. Find (a) the angle θ and (b) the tension in each string.

## Take Away | Suggested Reading

Hope you enjoy solving this numerical worksheet based on the Equilibrium chapter of Physics. For reference and further study, we suggest a few posts from this site.

**Suggested reading**

**Equilibrium – fundamentals and concepts****Floating body – stability conditions**