SOLID HEMISPHERE OF RADII R EACH, are placed in contact with each other with each other with their flat faces on a rough horizontal surface. A sphere of mass m and radius R is placed symmetrically on top of them. The normal reaction between the top sphere and any hemisphere assuming the system to be in state equilibrium is
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Consider a disk rotating in a horizontal plane with a constant angular speed “omega” about its center O.
The disk has a shaded region on one side of the diameter and an unshaded region on the other side.
When disk is in horizontal plane x-y with left half shaded and right half unshaded, 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 disk.
(i) they land back on the disk before the disk has completed one-eighth rotation,
(ii) their range is less than half the disk radius,and
(iii)”omega” remains constant throughout.
Then where will the two pebbles land?
(All are invited to answer this)