Choose the best answer

1. A horizontal lever is pivoted at its mid-point.
   Which of the following forces will result in
   a positive torque?
   
   1. An upward force upplied at the left end of the lever.
      
   2. A downward force applied at the right end of the lever
      
   3. A downward force applied at the left end of the lever.
      
   4. A downward force applied at the location of the pivot.
      
   5. An upward force applied at the location of the pivot
      
   Answer: C
   

2. Which of the following is not a correct statement?
   
   1. The center of gravity of an object is the point
      at which it can be balanced completely.
      
   2. Moment of inertia of a particle is equal to the
      product of its mass and the square of its
      perpendicular distance from the axis of rotation.
      
   3. Angular momentum of an object is equal the
      product of it moment of inertia and its
      angular velocity.
      
   4. Torque acting on an object is equal to the
      product of its mass and its angular
      acceleration.
      
   5. If the net torque acting on an object is zero,
      then its angular momentum is conserved.
      
   Answer: D
   

3. A horizontal lever of length 1.2 m is pivoted
   at its mid-point. Calculate the torque due to a force of 45 N
   pulling to the right at the right end of the
   lever.
   
   1. 27 N m
      
   2. 54 N m
      
   3. 0 N m
      
   4. -27 N m
      
   5. -54 N m
      
   Answer: C
   

4. A horizontal lever of length 4.5 m is pivoted at
   its mid-point. A 20 N downward force (force with
   downward vertical component) that makes an
   angle of 30 deg with the horizontal-left is acting
   at the left end of lever. Calculate the torque
   acting on the lever.
   
   1. 22.5 N m
      
   2. 29.067 N m
      
   3. 35.679 N m
      
   4. 3.473 N m
      
   5. 40.142 N m
      
   Answer: A
   

5. A uniform horizontal lever of length 5.2 m is
   pivoted at its mid-point. The following forces
   are acting on the lever: a 0.43 N vertically downward force
   acting at the right end of the lever, a 2 N
   vertically downward force acting at the left end of the
   lever, and a 2 N vertically downward force acting at a
   point on the lever 0.2 m away from the left end.
   Calculate the net torque acting on the lever.
   
   1. 20.527 N m
      
   2. 15.288 N m
      
   3. 8.882 N m
      
   4. 4.409 N m
      
   5. 19.137 N m
      
   Answer: C
   

6. A uniform horizontal lever of length 2 m is
   pivoted at its mid-point. The following forces
   are acting on the lever: a 0.23 N downward force (with downward
   vertical component) that makes an angle of 60 deg
   acting at the right end of the lever, a 2 N
   vertically downward force acting at the left end of the
   lever, and a 6 N vertically downward force acting at a
   point on the lever 0.5 m away from the left end.
   Calculate the net torque acting on the lever.
   
   1. 3.842 N m
      
   2. 4.801 N m
      
   3. 6.118 N m
      
   4. 8.099 N m
      
   5. 7.165 N m
      
   Answer: B
   

7. A uniform horizontal lever of length 2.83 m is pivoted
   at its mid-point. A vertically downward force of 5.71 N is
   acting at the right end of the lever. Calculate the vertically
   downward force that needs to be applied
   at a dstance of 0.27 m to the left of the pivot if the lever
   is to be in equilibrium?
   
   1. 36.226 N
      
   2. 29.925 N
      
   3. 47.826 N
      
   4. 44.797 N
      
   5. 15.524 N
      
   Answer: B
   

8. A uniform horizontal lever of length 2.8 m
   pivoted at its mid-point is in equilibrium. The following forces
   are acting on the lever: an unknown upward force (force with upward
   vertical component) that makes an angle of 40 deg with the
   horizontal-left acting at the right end of the lever, a 6 N
   vertically upward force acting at the left end of the
   lever, and an and a 4 N vertically downward force acting at a
   point on the lever 0.8 m away from the right end.
   Calculate the magnitude of the unknown force.
   
   1. 16.682 N
      
   2. 9.549 N
      
   3. 19.011 N
      
   4. 12.001 N
      
   5. 22.698 N
      
   Answer: D
   

9. Three particles of masses 7 kg, 9 kg and 5 kg are located
   at the points ( 12, 2 ) m, ( 1, 4 ) m, and ( -10, 5 ) m respectively.
   Determine the location of the center of gravity of the three
   particles.
   
   1. (0.725, 1.855) m
      
   2. (0.725, 3.571) m
      
   3. (2.048, 1.855) m
      
   4. (2.048, 3.571) m
      
   5. (3.872, 3.973) m
      
   Answer: D
   

10. The center of gravity of two particles of masses
    4.55 kg and 17.11 kg is located at the point ( 4, 1 ) m.
    The 4.55 kg particle is located at the point ( -5, -3 ) m.
    Find the location of the 17.11 kg particle.
    
    1. ( 6.393, 0.215 ) m
       
    2. ( 6.393, 2.064 ) m
       
    3. ( 3.614, 0.215 ) m
       
    4. ( 9.992, 1.642 ) m
       
    5. ( 3.614, 2.064 ) m
       
    Answer: B