A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring. the ring will then rotate with an angular velocity

Four identical thin rods each of mass M and length l , inertial form a square frame. moment of inertia of this frame about an axis through the centre of the square and perpendicular to this plane is 

• 4Ml²/3

• 2Ml²/3

• 13Ml²/3

• 13Ml²/3

A bar magnet having a magnetic moment of 2 x 10⁴ JT^-1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6 x 10^-4 T exists in the space. The work  is done in taking the magnet slowly from a direction parallel to the field to a direction 60^o from the field is

• 0.6 J

• 12 J

• 6 J

• 6 J

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is 

35.

A thin conducting ring and radius R is given charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is 

• 3E along KO

• E along OK

• E along KO

• E along KO

A thin rod of length L and Mass M is bent at its midpoint into two halves so that the angle between them is 90^o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is 

• ML²/24

• ML²/12

• ML²/6

• ML²/6

A Wheel has an angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of:

• 6

• 10

• 12

• 12

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A  is ml²/3, the initial angular acceleration of the rod will be:

• 2g/3l

• mgl/2

• 3gl/2

• 3gl/2

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is L_A when it is at A and L_B when it is B, then: 

• L_A > L_B

• L_A = L_B

• the relationship between L_A and L_B depends upon the slope of the line AB

• the relationship between L_A and L_B depends upon the slope of the line AB

One end of a string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards centre) will be (T represents the tension in the string)

• T

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