Q1: Centre of gravity of a thin hollow cone lies on the axis of symmmetry at a height of

ANS:B - one-third of the total height above base

the center of gravity of a thin hollow cone does not lie at one-third of the total height above the base. It actually lies at one-fourth of the total height above the base. To explain this:

1. Center of Gravity (CG) of a Cone: The center of gravity of a cone lies along its axis of symmetry. For a cone, the center of gravity is located one-fourth of the total height above the base, measured along the axis of symmetry.
2. Proof: You can derive this by considering the distribution of mass in the cone. The lower part of the cone has more mass closer to the base, and as you move up the cone, the mass decreases. The center of gravity is a point where the mass distribution is balanced in all directions.
3. Mathematical Representation: If the total height of the cone is H, then the center of gravity is located at a height of H/4​ above the base. This holds true for both solid and hollow cones.