A smooth cone is rotated with an angular velocity `omega` as shown. A block `A` is placed at height `h` . Block has no motion relative to cone. Choose the correct options, when `omega` is increased.

Options

A. net force acting on block will be more
B. normal reaction acting on block will be more
C. equilibrium height h will be lesser
D. normal reaction will remain unchanged

Answer

C, D

Explanation

`N cos theta = mg`
` N sin theta = m R omega^(2)`
From equation
`N = (mg)/(cos theta)` = constant as `theta` = constant
Net force is the resultant of N and mg and both forces are constant
Hence, net force is constant
`omega = sqrt((g)/(R ) tan theta)`
But `R = (h)/(tan theta)`
`:. omega = sqrt((g)/(h)) tan theta` or `omega prop (1)/(sqrt(h))` (`theta` = constant)