The magnitude of the normal force on a

block sliding along a horizontal circular path

on the inside of a friction-free cone

1. is equal to mg.

2. may be greater than mg.

3. may be less than mg.

4. is less than mg, always.

5. is greater than mg, always.

5. Is greater than mg, always

Explanation:

If the cone has an inclination of angle β, the sum of forces will be:

x-axis (centripetal axis):

N*sin β = m*ax  where ax is the centripetal acceleration

y-axis:

N*cos β - m*g = m*ay   where ay is the vertical acceleration. If the block starts falling down, ay will be negative. If the block starts sliding up, ay will be positive. If the block does not move up nor down, ay=0.

Solving for N:

If ay is positive or zero, N will be greater than mg. If ay is negative, N will be less than mg.

If the block is sliding along a horizontal circular path (not up, nor down), ay = 0, so N will always be greater than mg.