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Class 11  ยป  Physics  ยป  System of Particles and Rotational Motion

Equilibrium of Rigid Bodies - UNSOLVED PRACTICE SET

Class 11

Chapter: System of Particles and Rotational Motion | Topic: Equilibrium of Rigid Bodies

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Study Material.
Class 11

EQUILIBRIUM OF RIGID BODIES - UNSOLVED PRACTICE SET

Topic: Equilibrium of Rigid Bodies

Time: 40 mins | Marks: 30 | Difficulty: Medium

SECTION NAME

Q1. For a rigid body to be in translational equilibrium:

  1. The net torque must be zero
  2. The net force must be zero
  3. Both net force and net torque must be zero
  4. The body must be at rest

Q2. For a rigid body to be in complete equilibrium (both translational and rotational):

  1. ฮฃF = 0 only
  2. ฮฃฯ„ = 0 only
  3. ฮฃF = 0 and ฮฃฯ„ = 0
  4. The body must be stationary

Q3. A body is in stable equilibrium if, when slightly displaced:

  1. It returns to its original position
  2. It moves further away
  3. It stays in the new position
  4. It topples over

Q4. The centre of gravity of a body is the point where:

  1. The mass is concentrated
  2. The weight appears to act
  3. The centre of mass lies
  4. The torque is maximum

Q5. A uniform metre scale is balanced at its 50 cm mark. This is an example of:

  1. Stable equilibrium
  2. Unstable equilibrium
  3. Neutral equilibrium
  4. Dynamic equilibrium

Q6. When you place a pencil flat on your desk in the classroom, it stays there. But when you try to balance it on its tip, it falls. This shows that:

  1. The pencil is heavier at the bottom
  2. Balancing on the tip is unstable equilibrium
  3. Gravity doesn't act on the flat pencil
  4. The desk is not flat

Short Answer Questions

Q7. Distinguish between stable, unstable, and neutral equilibrium with one example of each.

Q8. State the conditions for complete equilibrium of a rigid body. Write them in mathematical form.

Q9. A uniform rod of weight W is supported at two points. Draw the free body diagram and write the equilibrium conditions.

Q10. Explain why a racing car has a low centre of gravity and a wide wheelbase.

Q11. A ladder leans against a smooth wall with its base on rough ground. Draw the free body diagram and identify all forces acting on the ladder.

Q12. Why is it easier to tip over a tall cupboard than a short one of the same base area?

Long Answer Questions

Q13. Discuss the three types of equilibrium with examples:

(i) Stable equilibrium

(ii) Unstable equilibrium

(iii) Neutral equilibrium

For each type, explain:

The condition for the type of equilibrium in terms of potential energy

What happens when the body is slightly displaced

One real-life example from everyday life or engineering

Also explain the role of the position of the centre of gravity in determining the type of equilibrium.

Q14. A uniform ladder of length L and mass M rests against a smooth vertical wall with its base on rough horizontal ground. The coefficient of friction between the ladder and ground is ฮผ. The ladder makes angle ฮธ with the horizontal.

(i) Draw a clear free body diagram showing all forces.

(ii) Write the conditions for equilibrium.

(iii) Find the normal reaction at the wall.

(iv) Find the minimum angle ฮธ at which the ladder will not slip.

(v) What happens if a person climbs up the ladder?

Q15. A student builds a mobile for her school art project using a uniform rod of mass 0.2 kg and length 0.6 m.

(i) She suspends a 0.3 kg mass at one end. Where should she suspend the rod from a string so that it balances horizontally?

(ii) She adds another 0.2 kg mass at the other end. Where is the new suspension point?

(iii) She wants to hang a 0.1 kg decoration at the 20 cm mark. How does this affect the balance?

(iv) Explain how the concept of torque is used to solve this problem.

Numerical / Application-Based Problems

Q16. A uniform beam of length 4 m and mass 20 kg is supported at its two ends. A boy of mass 40 kg stands 1 m from one end.

(i) Draw the free body diagram.

(ii) Calculate the reactions at the two supports.

(iii) Where should the boy stand so that the reactions are equal?

(iv) What is the maximum mass the boy can have if he stands at the centre without breaking the beam? (The beam can withstand maximum 300 N force at each support)

(v) If the right support is moved 0.5 m inward, recalculate the reactions when the boy stands 1 m from the left end.

Q17. A uniform ladder of length 5 m and mass 15 kg leans against a smooth vertical wall at an angle of 60ยฐ to the horizontal. The coefficient of static friction between the ladder and the ground is 0.4.

(i) Draw the free body diagram.

(ii) Calculate the normal reactions at the wall and the ground.

(iii) Calculate the frictional force at the ground.

(iv) Calculate the minimum angle at which the ladder will not slip.

(v) A person of mass 60 kg climbs up to the midpoint of the ladder. Does the ladder slip? Verify.

(Given: g = 9.8 m/sยฒ)

Q18. In a school seesaw (teeter-totter), a uniform plank of mass 30 kg and length 3 m is pivoted at its centre. Two students, A (mass 40 kg) and B (mass 50 kg), sit on opposite ends.

(i) Calculate the initial torque about the pivot. Which side goes down?

(ii) Where should student A move to balance the seesaw?

(iii) A third student C (mass 35 kg) joins and sits with A. Where should A and C sit together to balance the seesaw if B remains at the end?

(iv) The pivot is shifted 0.3 m towards B. Where should A sit now to balance with B at the end?

(v) Explain why the seesaw is designed with the pivot at the centre rather than at one end.


Total: 30 Marks | Time: 40 mins

Explore more topics in System of Particles and Rotational Motion

Centre of Mass Definition and Position Motion of Centre of Mass Angular Velocity and Angular Acceleration Torque and Angular Momentum Conservation of Angular Momentum Moment of Inertia and Radius of Gyration Theorems Parallel and Perpendicular Axis Rolling Motion Without Slipping