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.

 

 

 

Dear student


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
 

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