Question

A smooth cone is rotated with an angular velocity $\omega$ as shown. A block $A$ is placed at height $h$. The block has no motion relative to the cone. Now $\omega$ is increased. Choose the correct options.

• A. net force acting on block will increase
• B. normal reaction acting on block will increase
• C. $h$ will increase
• D. normal reaction will remain unchanged

Answer 1

Answer: (A), (B), (C)

The correct options are
A net force acting on block will increase
B normal reaction acting on block will increase
C $h$ will increase

FBD of the block:


Block is performing horizontal circular motion.
$\therefore N\cos \theta =mg$ ... (i)
and $N\sin \theta =m{a}_c=m{\omega }^{2}r$ ... (ii)
Net force on body $=\overrightarrow{N}+\overrightarrow{mg}$

If $\omega$ increases, $N\sin \theta$ has to also increase. Since $\theta$ doesn't change, $N$ will increase
So, net force acting on block will increase.

Also the vertical component $N\cos \theta$ will increase, which will accelerate the body in $y-$ direction/vertical.
So height $h$ above the ground will increase.
$\therefore$ correct options $\Rightarrow$ (a), (b), (c).