If the net external forces acting on the system of particles is zero, then which of the following may vary ?

1. Momentum of the system

2. Velocity of centre of mass

3. Position of centre of mass

4. None of the above

Subtopic:  Center of Mass |
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A constant torque of 1000 N-m turns a wheel of moment of inertial 200 kg-m2 about an axis through its centre. Its angular velocity after 3 s is

1. 1 rad/s

2. 5 rad/s

3. 10 rad/s

4. 15 rad/s

Subtopic:  Torque |
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Point masses m1 and m2 are placed at the opposite ends of a rigid of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ω0 is minimum is given by

1. x =m1m2L2. x = m2m1L3. x = m2Lm1+ m24. x = m1Lm1+ m2

Subtopic:  Rotational Motion: Dynamics |
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A circular disc of radius r has a uniform thickness.  A circular hole of diameter equal to the radius of the disc has been cut out as shown.  The centre of gravity of the remaining disc lies on the diameter of the disc at a distance x to the left of the centre of the original disc.  The value of x is

1. r                             

2. r2

3. r4                         

 4. r6

 

Subtopic:  Center of Mass |
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A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force 'F' is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

                 

1.  43l

2.  I

3.  23l

4.  32l

Subtopic:  Center of Mass |
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A wheel is rotating about an axis through its centre at 720 r.p.m. It is acted upon by a constant torque opposing its motion for 8 seconds to bring it to rest finally. The value of torque in Nm is: (given l = 24π kg m2)

1. 48

2. 72

3. 96

4. 120

Subtopic:  Rotational Motion: Dynamics |
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Assertion : The speed of whirlwind in a tornado is alarmingly high.

Reason    : If no external torque acts on a body, its angular velocity remains conserved.

1. If both assertion and reason are true and reason is the correct explanation of assertion.

2. If both assertion and reason are true but reason is not the correct explanation of assertion.

3. If assertion is true but reason is false.

4. If both assertion and reason are false.

Subtopic:  Angular Momentum |
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A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 2r and thickness t4. The relation between moments of inertia IA and IB is

1.  IA > IB

2.  IA = IB

3.  IA < IB

4.  Depends on the actual values of t and r

Subtopic:  Moment of Inertia |
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A particle of mass 2 kg located at the position (i^+ j^) m has a velocity of 2(+i^ - j^ +k^) m/s. Its angular momentum about z-axis in kg-m2/s is :

1. +4

2. +8

3. -4

4. -8

Subtopic:  Angular Momentum |
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A cylinder of mass 'M' is suspended by two strings wrapped around it as shown. The acceleration 'a' and the tension T when the cylinder falls and the string unwinds itself are, respectively,
             

1.  a = g, T = Mg2

2.  a = g2, T = Mg2

3.  a = g3, T = Mg3

4.  a = 2g3, T = Mg6

Subtopic:  Rolling Motion |
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