Equilibrium and Elasticity - Chapter No 11

Right Answers have been shown below in red color.

1. A net torque applied to a rigid object always tends to produce:

A. linear acceleration
B. rotational equilibrium
C. angular acceleration
D. rotational inertia
E. none of these

2. The conditions that the net force and the net torque both vanish:

A. hold for every rigid body in equilibrium
B. hold only for elastic solid bodies in equilibrium
C. hold for every solid body
D. are always sufficient to calculate the forces on a solid object in equilibrium
E. are sufficient to calculate the forces on a solid object in equilibrium only if the object is elastic

3. For an object in equilibrium the net torque acting on it vanishes only if each torque is calculated about:

A. the center of mass
B. the center of gravity
C. the geometrical center
D. the point of application of the force
E. the same point

4. For a body to be in equilibrium under the combined action of several forces:

A. all the forces must be applied at the same point
B. all of the forces form pairs of equal and opposite forces
C. the sum of the components of all the forces in any direction must equal zero
D. any two of these forces must be balanced by a third force
E. the lines of action of all the forces must pass through the center of gravity of the body

5. For a body to be in equilibrium under the combined action of several forces:

A. all the forces must be applied at the same point
B. all of the forces form pairs of equal and opposite forces
C. any two of these forcesmust be balanced by a third force
D. the sum of the torques about any point must equal zero
E. the lines of action of all the forces must pass through the center of gravity of the body

6. To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at:

A. the center of mass
B. the geometrical center
C. the center of gravity
D. a point on the boundary
E. none of the above

7. The center of gravity coincides with the center of mass:

A. always
B. never
C. if the center of mass is at the geometrical center of the body
D. if the acceleration due to gravity is uniform over the body
E. if the body has a uniform distribution of mass

8. The location of which of the following points within an object might depend on the orientation of the object?

A. Its center of mass
B. Its center of gravity
C. Its geometrical center
D. Its center of momentum
E. None of the above

9. A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its geometrical center, is:

A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above

10. A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above

11. A cube balanced with one edge in contact with a table top and with its center of gravity  directly above the edge is in equilibrium with respect to rotation about the edge and in equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.

A. stable, stable
B. stable, unstable
C. unstable, stable
D. unstable, unstable
E. unstable, neutral

12. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force F1 is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force F2 (not shown) is applied perpendicularly at the 100-cm end of the stick. The forces are horizontal. If the stick does not move, the force exerted by the pivot on the stick:

Equilibrium and Elasticity

A. must be zero
B. must be in the same direction as Fn1 and have magnitude |F2| − |F1|
C. must be directed opposite to Fn1 and have magnitude |F2| − |F1|
D. must be in the same direction as Fn1 and have magnitude |F2| + |F1|
E. must be directed opposite to F1 and have magnitude |F2| + |F1|

13. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force F1 is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force F2 (not shown) is applied perpendicularly at the 60-cm mark. The forces are horizontal. If the stick does not move, the force exerted by the pivot on the stick:

Equilibrium and Elasticity

A. must be zero
B. must be in the same direction as Fn1 and have magnitude |F2| − |F1|
C. must be directed opposite to F and have magnitude 1 | F2| − | F1|
D. must be in the same direction as F1 and have magnitude |F2| + |F1|
E. must be directed opposite to F1 and have magnitude |F2| + |F1|

14. Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods and all equal in magnitude. Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?

Equilibrium and Elasticity 1

A. Only 1
B. Only 2
C. Only 3
D. Only 1 and 2
E. All three

15. A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N. The magnitude of the tension force of each of the two supporting ropes is:

A. 60 N
B. 94 N
C. 120 N
D. 190 N
E. 260 N

16. The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a rope (AE) and friction between the rod and the wall. To use a single equation to find the force exerted on the rod by the rope at which point should you place the reference point for
computing torque?

Equilibrium and Elasticity 2

C is the Right Answer

17. A picture P of weight W is hung by two strings as shown. The magnitude of the tension force of each string is T. The total upward pull of the strings on the picture is:

Equilibrium and Elasticity 3

A. 2W cos θ
B. T sin θ
C. T cos θ
D. 2T sin θ
E. 2T cos θ

18. A picture can be hung on a wall with string in three different ways, as shown. The magnitude of the tension force of the string is:

Equilibrium and Elasticity 4

A. least in I
B. greatest in I
C. greatest in II
D. least in III
E. greatest in III

19. A uniform plank is supported by two equal 120-N forces at X and Y, as shown. The support at X is then moved to Z (half-way to the plank center). The supporting forces at Y and Z are then:

Equilibrium and Elasticity 6

A. FY = 240 N, FZ = 120 N
B. FY = 200 N, FZ = 40 N
C. FY = 40 N, FZ = 200 N
D. FY = 80 N, FZ = 160 N
E. FY = 160 N, FZ = 80 N

20. A uniform rod AB is 1.2 m long and weighs 16 N. It is suspended by strings AC and BD as shown. A block P weighing 96 N is attached at E, 0.30 m from A. The magnitude of the tension force of the string BD is:

Equilibrium and Elasticity 5

A. 8.0 N
B. 24 N
C. 32 N
D. 48 N
E. 80 N

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