Biology Forums - Study Force

Two blocks, m₁ = 1.0 kg and m₂ = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its rotational inertia is 5.0 kgm², the acceleration of the system is
 
 
 
   
  a.
  (1/6)g
   
  b.
  (3/8)g
   
  c.
  (1/8)g
   
  d.
  (1/2)g
   
  e.
  (5/8)g

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[Ques. 2]

In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kgm²/s) at the lowest point of its path relative to the center of the circle is approximately
 
   

   
  a.
  40
   
  b.
  10
   
  c.
  30
   
  d.
  20
   
  e.
  50

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[Ques. 3] A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel and tangent to the cylinder, as shown below. The rotational inertia of the cylinder about this axis is
 
 
 
   
  a.
  .
   
  b.
  .
   
  c.
  MR².
   
  d.
  .
   
  e.
  .

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[Ques. 4] A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The rotational inertia of the sphere about this axis is
 
 
 
   
  a.
  .
   
  b.
  .
   
  c.
  .
   
  d.
  .
   
  e.
  .

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[Ques. 5]

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.
 
   

   
  a.
  2.9 J
   
  b.
  2.6 J
   
  c.
  3.1 J
   
  d.
  3.4 J
   
  e.
  1.6 J

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[Ques. 6]

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.
 
   

   
  a.
  18 J
   
  b.
  15 J
   
  c.
  12 J
   
  d.
  23 J
   
  e.
  26 J

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[Ques. 7] If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the rotational inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.
 
 
 
   
  a.
  3.7 kgm²
   
  b.
  2.8 kgm²
   
  c.
  3.2 kgm²
   
  d.
  2.3 kgm²
   
  e.
  3.9 kgm²

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[Ques. 8] A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s². What is the rotational inertia of the wheel?
 
 
 
   
  a.
  0.023 kgm²
   
  b.
  0.027 kgm²
   
  c.
  0.016 kgm²
   
  d.
  0.019 kgm²
   
  e.
  0.032 kgm²

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[Ques. 9] A mass (M₁ = 5.0 kg) is connected by a light cord to a mass (M₂ = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M₂ is 3.5 m/s². What is the rotational inertia of the pulley?
 
 
 
   
  a.
  0.29 kgm²
   
  b.
  0.42 kgm²
   
  c.
  0.20 kgm²
   
  d.
  0.62 kgm²
   
  e.
  0.60 kgm²

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[Ques. 10]

An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux _B through any area completely inside the solenoid, centered on the solenoid axis but at a 45 angle to the axis, so that it touches the inside of the solenoid, as shown below, is
 
   

   
  a.
  .
   
  b.
  .
   
  c.
  ₀a²nI.
   
  d.
  2₀a²nI.
   
  e.
  0.

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