From a circular disc of radius R and mass 9M, a small disc of mass M and radius R/3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

• 40MR²/9

• MR²

• 4 MR²

• 4 MR²

A closely wound solenoid of 2000 turns and area of cross -section 1.5 x 10^-4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 x 10^-2 T making an angle of 30^o with axis of  the solenoid. The torque on the solenoid will be

• 3 x 10^-3 N-m

• 1.5 x 10^-3 N-m

• 1.5 x 10^-2 N-m

• 1.5 x 10^-2 N-m

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

• (M +2m)ω /2m

• 2Mω / M + 2m

• (M +2m)ω / M

• (M +2m)ω / M

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle

• depends on v and not on R

• depends on R and not on v

• is independent of both v and R

• is independent of both v and R

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 

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