The moment of inertia of a thin rectangular plate \(\text {ABCD}\) of uniform thickness about an axis passing through the centre \(\text O\) and perpendicular to the plane of the plate is 

                             

1.  \(\text I_{1}   +   \text I_{2}\)

2.  \(\text I_{2}   +  \text I_{4}\)

3.  \(\text I_{1}   - \text   I_{3}\)

4.  \(\text I_{1}   +\text   I_{2  } +  \text I_{3}   + \text   I_{4}\)

Subtopic:  Moment of Inertia |
 65%
From NCERT
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The centre of a wheel rolling on a plane surface moves with a speed \(v_0.\) A particle on the rim of the wheel at the same level as the centre will be moving at speed:
1. zero
2. \(v_0\)
3. \(\sqrt{2}v_0\)
4. \(2v_0\)

Subtopic:  Rolling Motion (OLD NCERT) |
 62%
From NCERT
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Moment of inertia of a uniform cylinder of mass M, radius R and length l about an axis passing through its center and normal to its axis would be

1.  Ml212

2.  MR22

3.  Ml212 + R24

4.  Ml212 + R22

Subtopic:  Moment of Inertia |
 58%
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A particle moves along a circle of radius 20πm with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is

1. 640 π m/s2

2. 160 π m/s2

3. 40 π m/s2

4. 40 m/s2

Subtopic:  Rotational Motion: Kinematics |
 57%
From NCERT
PMT - 2003
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If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:

1. 6 hours 2. 12 hours
3. 18 hours 4. 24 hours
Subtopic:  Angular Momentum |
 70%
From NCERT
PMT - 1999
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If a force acts on a body at a point away from the centre of mass, then 

1.  Linear acceleration changes 

2.  Angular acceleration changes 

3.  Both change 

4.  None of these

Subtopic:  Torque |
 60%
From NCERT
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If the linear density of a rod of length \(3~ \text{m}\) varies as \(\lambda=2+x,\) then the position of the centre-of-mass of the rod is at a distance of:
1. \(\dfrac{7}{3}~\text{m}\) 2. \(\dfrac{10}{7}~\text{m}\)
3. \(\dfrac{12}{7}~\text{m}\) 4. \(\dfrac{9}{7}~\text{m}\)
Subtopic:  Center of Mass |
 67%
From NCERT
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A sphere can not roll on:

1.  a smooth horizontal surface 

2.  a rough horizontal surface 

3.  a smooth inclined surface 

4.  a rough inclined surface 

Subtopic:  Rolling Motion (OLD NCERT) |
 55%
From NCERT
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Two balls are thrown simultaneously in the air. The acceleration of the center of mass of the two balls while in air 

1.  depends on the direction of the motion of the balls 

2.  depends on the masses of the two balls 

3.  depends on the speeds of two balls 

4.  is equal to g 

Subtopic:  Center of Mass |
 68%
From NCERT
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A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizotal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

1. 2ghI+mr

2. 2mghI+mr2

3. 2mghI+2m12

4. 2gh

Subtopic:  Rolling Motion (OLD NCERT) |
 73%
From NCERT
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