Aparticle of mass 1 g executes an oscillatory motion on the concave surface of a spherical dish of radius 2m placed on a horizontal plane, Figure . If the motion of the particle begins from a point on the dis at a height of 1 cm. from the horizontal plane and coefficient of friction is 0.01 , fing the total distance covered by the particle before coming to rest.

Explanation

In figure, `CO=CA=200cm,`
`OB=1cm. `
`:. BC=CO-OB=200-1=199cm.`
In `DeltaABC, costheta=(BC)/(AC)=(199)/(200)`
Treating the dish an an inclined plane, and using the principle of energy conservation, i.e.,
Loss in P.E. `=` work done agains friction
`mgh=muRxxs=mu mg cos theta xxs`
`s=(mgh)/(mu mg costheta)=(h)/(mucostheta)`
`s=(1//100)/(0.01xx199//200)=(200)/(199)=1.005m`