When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is `80 cm` and for rotation less than `1 rev`, what are the
(i) smallest and
(ii) largest angular speeds that cause the toast to hit and then topple to be butter-side down ?

When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 76 cm and for rotation less than 1 rev, what are the (a) smallest and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down?

Consider a disc rotating in the horizontal plane with a constant angular speed omega about its centre O . The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed (1)/(8) rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then

Consider a disc rotating in the horizontal plane with a constant angular speed omega about its centre O . The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed (1)/(8) rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then

Consider a disc rotating in the horizontal plane with a constant angular speed omega about its centre O . The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed (1)/(8) rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then

A 100 turn closely wound circular coil of radius 10cm carries a current of 3*2A . (i) What is the field at the centre of the coil? (ii) What is the magnetic moment of this arrangement? The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A uniform magnetic field of 2T in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90^@ under the influence of the magnetic field. (iii) What are the magnitudes of the torques on the coil in the initial and final positions? (iv) What is the angular speed acquired by the coil when it has rotated by 90^@ ? The moment of inertia of the coil is 0*1kgm^2 .

Consider a disc rotating in the horizontal plane with a constant angular speed omega about its center O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1//8 rotation, (ii) their range is less than half the disc radius, and (iii) omega remains constant throughout. Then