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 =m1m2L
2. x = m2m1L
3. x = m2Lm1+ m2
4. x = m1Lm1+ m2

Subtopic:  Rotational Motion: Dynamics |
 78%
From NCERT
AIPMT - 2015
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Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s-1. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s-1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s-1) of the system is

1. 60

2. 100

3. 120

4. 40

Subtopic:  Angular Momentum |
 74%
From NCERT
NEET - 2013
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A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

1.  Disk

2.   Sphere

3.  Both reach at the same time

4.  Depends on their masses

Subtopic:  Rolling Motion (OLD NCERT) |
 70%
From NCERT
NEET - 2016
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A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in horizontal position. Given that the moment of inerita of the rod about A is ml23 the initial angular acceleration of the rod will be
                           

1. 2g3l
2. mgl2
3. 32gl
4. 3g2l

Subtopic:  Torque |
 73%
From NCERT
NEET - 2013
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Two rotating bodies \(A\) and \(B\) of masses \(m\) and \(2m\) with moments of inertia \(I_A\) and \(I_B\) \((I_B>I_A)\) have equal kinetic energy of rotation. If \(L_A\) and \(L_B\) be their angular momenta respectively, then:
1. \(L_{A} = \frac{L_{B}}{2}\)
2. \(L_{A} = 2 L_{B}\)
3. \(L_{B} > L_{A}\)
4. \(L_{A} > L_{B}\)

Subtopic:  Rotational Motion: Dynamics |
 72%
From NCERT
NEET - 2016
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A solid sphere of mass m and radius R is rotating about its diameter. A soild cyclinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation Esphere/Ecylinder  will be 

1. 2:3

2. 1:5

3. 1:4

4. 3:1

Subtopic:  Moment of Inertia |
 80%
From NCERT
NEET - 2016
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A light rod of length l has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is 

1.  m1m2m1+m2l2

2. m1+m2m1m2l2l2

3. m1+m2l2

4. m1m2l2 

Subtopic:  Moment of Inertia |
 76%
From NCERT
NEET - 2016
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From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre ?

1. 13 MR2/32       

2. 11 MR2/32

3. 9 MR2/32         

4. 15 MR2/32

Subtopic:  Moment of Inertia |
 57%
NEET - 2016
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A force \(\vec{F}=\alpha\hat i+3\hat j+6\hat k\) is acting at a point \(\vec{r}=2\hat i-6\hat j-12\hat k.\) The value of \(\alpha\) for which angular momentum is conserved about the origin is:
1. \(-1\)
2. \(2\)
3. zero
4. \(1\)

Subtopic:  Angular Momentum |
 68%
From NCERT
NEET - 2015
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An automobile moves on a road with a speed of 54 km h-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is 

(1)6.66 kgm2s-2

(2)8.58 kgm2s-2

(3)10.86 kgm2s-2

(4)2.86 kgm2s-2

Subtopic:  Torque |
 74%
From NCERT
NEET - 2015
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