Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

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 $${1 \over 8}$$ rotation, (ii) their range is less than half the disc radius, and (iii) $$\omega $$ remains constant throughout. Then

A loop carrying current $$l$$ lies in the xy-plane as shown in the figure. The unit vector $$\widehat k$$ is coming out of the plane of the paper. The magnetic moment of the current loop is