A hemispherical bowl of radius 10 m rotates about its vertical axis with an angular velocity 1 4 rad/s - Physics - Kinematics

Question

A hemispherical bowl of radius 10 m rotates about its vertical
axis with an angular velocity 1 4 rad/s A point particle of mass
10-2 kg placed on the smooth inner surface of the bowl, also
rotates with the same speed The particle is at a height h from the
bottom of the bowl Find the height of the particle

Rajnish Kumar · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_591b3e677b67a%20jpg"
style="width: 250px; height: 195px;">

let particle is height h from botton and making angle θ with vertical from centre of hemispherenow let vertical distance from top plane of hemisphere is x as shown in figure now writing eq on both axis X, Y Nsinθ=mω2rNcosθ=mgdividing both above eqtanθ=ω2rgrx=ω2rg1x=ω2gx=gω2=9
8(1 4)2=5so h=R-x=10-5=5 m Regards