What should be the conditions under which someone wins a match of Tug-Of-War regarding the weight and force applied on the rope?
The One who applies more friction force (shear force) on the ground will win because friction will resist the slipping between the surface and the person.
What is the difference between the center of Buoyancy and center of Mass?
The center of buoyancy for an object is the center of mass for the fluid it displaces. Whereas center of gravity is a point from which the weight of a system can be considered to act.
Two identical conducting rings A&C of radius r are in pure rolling over a horizontal conducting plane with the same speed(of their center of mass) "v" but in opposite direction. A constant magnetic field B is present pointing inside the plane of the paper. Then calculate the potential difference between highest points of the two rings in terms of B, v, and r
4Bvr is the answer. Consider rotation of the rings about their lowest points diametrically. e = [Bw(omega)(2r)^2] / 2 = 2Bvr at A with respect to plane (since pure rotation). and e = -2Bvr at B with respect to the plane. So, the potential difference between these two points = 4Bvr.